LMFDB - Embedded newform 430.2.k.a.121.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [430,2,Mod(11,430)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(430, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([0, 10]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("430.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 430 = 2 \cdot 5 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	430.k (of order $7$, degree $6$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$3.43356728692$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{7})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 3 x^{11} + 6 x^{10} - 16 x^{9} + 44 x^{8} - 70 x^{7} + 141 x^{6} - 182 x^{5} + 270 x^{4} + \cdots + 1 $ x^12 - 3x^11 + 6x^10 - 16x^9 + 44x^8 - 70x^7 + 141x^6 - 182x^5 + 270x^4 - 124x^3 + 115x^2 + 20*x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{7}]$

Embedding invariants

Embedding label			121.1
Root			$-0.0765242 + 0.0368521i$ of defining polynomial
Character	$\chi$	$=$	430.121
Dual form			430.2.k.a.231.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.222521 + 0.974928i) q^{2} +(-0.296379 - 1.29852i) q^{3} +(-0.900969 - 0.433884i) q^{4} +(0.623490 - 0.781831i) q^{5} +1.33192 q^{6} -3.79472 q^{7} +(0.623490 - 0.781831i) q^{8} +(1.10459 - 0.531942i) q^{9} +O(q^{10})$	\(q+(-0.222521 + 0.974928i) q^{2} +(-0.296379 - 1.29852i) q^{3} +(-0.900969 - 0.433884i) q^{4} +(0.623490 - 0.781831i) q^{5} +1.33192 q^{6} -3.79472 q^{7} +(0.623490 - 0.781831i) q^{8} +(1.10459 - 0.531942i) q^{9} +(0.623490 + 0.781831i) q^{10} +(-2.19641 + 1.05773i) q^{11} +(-0.296379 + 1.29852i) q^{12} +(-0.277479 + 0.347948i) q^{13} +(0.844405 - 3.69958i) q^{14} +(-1.20001 - 0.577896i) q^{15} +(0.623490 + 0.781831i) q^{16} +(-3.59738 - 4.51097i) q^{17} +(0.272811 + 1.19526i) q^{18} +(-3.07848 - 1.48252i) q^{19} +(-0.900969 + 0.433884i) q^{20} +(1.12468 + 4.92753i) q^{21} +(-0.542468 - 2.37671i) q^{22} +(-5.17241 + 2.49090i) q^{23} +(-1.20001 - 0.577896i) q^{24} +(-0.222521 - 0.974928i) q^{25} +(-0.277479 - 0.347948i) q^{26} +(-3.50942 - 4.40068i) q^{27} +(3.41893 + 1.64647i) q^{28} +(0.396418 - 1.73682i) q^{29} +(0.830435 - 1.04133i) q^{30} +(-0.394434 + 1.72813i) q^{31} +(-0.900969 + 0.433884i) q^{32} +(2.02446 + 2.53859i) q^{33} +(5.19836 - 2.50340i) q^{34} +(-2.36597 + 2.96683i) q^{35} -1.22600 q^{36} -3.78111 q^{37} +(2.13037 - 2.67140i) q^{38} +(0.534056 + 0.257188i) q^{39} +(-0.222521 - 0.974928i) q^{40} +(1.05623 - 4.62764i) q^{41} -5.05425 q^{42} +(4.09757 - 5.11956i) q^{43} +2.43783 q^{44} +(0.272811 - 1.19526i) q^{45} +(-1.27748 - 5.59700i) q^{46} +(3.12145 + 1.50321i) q^{47} +(0.830435 - 1.04133i) q^{48} +7.39993 q^{49} +1.00000 q^{50} +(-4.79140 + 6.00822i) q^{51} +(0.400969 - 0.193096i) q^{52} +(0.499153 + 0.625919i) q^{53} +(5.07126 - 2.44219i) q^{54} +(-0.542468 + 2.37671i) q^{55} +(-2.36597 + 2.96683i) q^{56} +(-1.01268 + 4.43685i) q^{57} +(1.60506 + 0.772957i) q^{58} +(0.301636 + 0.378239i) q^{59} +(0.830435 + 1.04133i) q^{60} +(-0.824581 - 3.61273i) q^{61} +(-1.59703 - 0.769089i) q^{62} +(-4.19161 + 2.01857i) q^{63} +(-0.222521 - 0.974928i) q^{64} +(0.0990311 + 0.433884i) q^{65} +(-2.92543 + 1.40881i) q^{66} +(-1.54476 - 0.743918i) q^{67} +(1.28389 + 5.62508i) q^{68} +(4.76748 + 5.97823i) q^{69} +(-2.36597 - 2.96683i) q^{70} +(10.8265 + 5.21375i) q^{71} +(0.272811 - 1.19526i) q^{72} +(8.88454 - 11.1409i) q^{73} +(0.841377 - 3.68631i) q^{74} +(-1.20001 + 0.577896i) q^{75} +(2.13037 + 2.67140i) q^{76} +(8.33476 - 4.01381i) q^{77} +(-0.369579 + 0.463437i) q^{78} +4.26059 q^{79} +1.00000 q^{80} +(-2.38105 + 2.98575i) q^{81} +(4.27658 + 2.05949i) q^{82} +(1.52492 + 6.68112i) q^{83} +(1.12468 - 4.92753i) q^{84} -5.76974 q^{85} +(4.07941 + 5.13404i) q^{86} -2.37279 q^{87} +(-0.542468 + 2.37671i) q^{88} +(1.95777 + 8.57754i) q^{89} +(1.10459 + 0.531942i) q^{90} +(1.05296 - 1.32037i) q^{91} +5.74094 q^{92} +2.36091 q^{93} +(-2.16011 + 2.70869i) q^{94} +(-3.07848 + 1.48252i) q^{95} +(0.830435 + 1.04133i) q^{96} +(-10.0228 + 4.82674i) q^{97} +(-1.64664 + 7.21440i) q^{98} +(-1.86348 + 2.33672i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 2 q^{2} - q^{3} - 2 q^{4} - 2 q^{5} - 8 q^{6} + 4 q^{7} - 2 q^{8} + 7 q^{9}+O(q^{10}) $ 12 * q - 2 * q^2 - q^3 - 2 * q^4 - 2 * q^5 - 8 * q^6 + 4 * q^7 - 2 * q^8 + 7 * q^9	\( 12 q - 2 q^{2} - q^{3} - 2 q^{4} - 2 q^{5} - 8 q^{6} + 4 q^{7} - 2 q^{8} + 7 q^{9} - 2 q^{10} + 3 q^{11} - q^{12} - 4 q^{13} - 10 q^{14} - q^{15} - 2 q^{16} - 5 q^{17} - 2 q^{19} - 2 q^{20} + 22 q^{21} - 4 q^{22} - 16 q^{23} - q^{24} - 2 q^{25} - 4 q^{26} + 8 q^{27} + 11 q^{28} + 2 q^{29} + 6 q^{30} + 27 q^{31} - 2 q^{32} + 6 q^{33} + 2 q^{34} - 3 q^{35} - 18 q^{37} - 2 q^{38} + 5 q^{39} - 2 q^{40} + 14 q^{41} - 20 q^{42} + 14 q^{43} - 4 q^{44} - 16 q^{46} + 2 q^{47} + 6 q^{48} - 12 q^{49} + 12 q^{50} - 5 q^{51} - 4 q^{52} + 2 q^{53} - 6 q^{54} - 4 q^{55} - 3 q^{56} - 19 q^{57} + 2 q^{58} + 4 q^{59} + 6 q^{60} + 16 q^{61} - 22 q^{62} + 13 q^{63} - 2 q^{64} + 10 q^{65} - 8 q^{66} + 9 q^{67} + 9 q^{68} - 15 q^{69} - 3 q^{70} + 27 q^{71} + 28 q^{73} + 24 q^{74} - q^{75} - 2 q^{76} + 26 q^{77} + 5 q^{78} + 10 q^{79} + 12 q^{80} - 12 q^{81} + 7 q^{82} - 31 q^{83} + 22 q^{84} - 12 q^{85} - 28 q^{86} - 6 q^{87} - 4 q^{88} - 38 q^{89} + 7 q^{90} + 8 q^{91} + 12 q^{92} - 2 q^{93} - 12 q^{94} - 2 q^{95} + 6 q^{96} - 15 q^{97} - 19 q^{98} - 6 q^{99}+O(q^{100}) \) 12 * q - 2 * q^2 - q^3 - 2 * q^4 - 2 * q^5 - 8 * q^6 + 4 * q^7 - 2 * q^8 + 7 * q^9 - 2 * q^10 + 3 * q^11 - q^12 - 4 * q^13 - 10 * q^14 - q^15 - 2 * q^16 - 5 * q^17 - 2 * q^19 - 2 * q^20 + 22 * q^21 - 4 * q^22 - 16 * q^23 - q^24 - 2 * q^25 - 4 * q^26 + 8 * q^27 + 11 * q^28 + 2 * q^29 + 6 * q^30 + 27 * q^31 - 2 * q^32 + 6 * q^33 + 2 * q^34 - 3 * q^35 - 18 * q^37 - 2 * q^38 + 5 * q^39 - 2 * q^40 + 14 * q^41 - 20 * q^42 + 14 * q^43 - 4 * q^44 - 16 * q^46 + 2 * q^47 + 6 * q^48 - 12 * q^49 + 12 * q^50 - 5 * q^51 - 4 * q^52 + 2 * q^53 - 6 * q^54 - 4 * q^55 - 3 * q^56 - 19 * q^57 + 2 * q^58 + 4 * q^59 + 6 * q^60 + 16 * q^61 - 22 * q^62 + 13 * q^63 - 2 * q^64 + 10 * q^65 - 8 * q^66 + 9 * q^67 + 9 * q^68 - 15 * q^69 - 3 * q^70 + 27 * q^71 + 28 * q^73 + 24 * q^74 - q^75 - 2 * q^76 + 26 * q^77 + 5 * q^78 + 10 * q^79 + 12 * q^80 - 12 * q^81 + 7 * q^82 - 31 * q^83 + 22 * q^84 - 12 * q^85 - 28 * q^86 - 6 * q^87 - 4 * q^88 - 38 * q^89 + 7 * q^90 + 8 * q^91 + 12 * q^92 - 2 * q^93 - 12 * q^94 - 2 * q^95 + 6 * q^96 - 15 * q^97 - 19 * q^98 - 6 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/430\mathbb{Z}\right)^\times$.

$n$	$87$	$261$
$\chi(n)$	$1$	$e\left(\frac{3}{7}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.222521	+	0.974928i	−0.157346	+	0.689378i
$2$	−0.222521	+	0.974928i	−0.157346	+	0.689378i
$3$	−0.296379	−	1.29852i	−0.171114	−	0.749702i	−0.985541	−	0.169435i	$-0.945806\pi$
$3$	−0.296379	−	1.29852i	−0.171114	−	0.749702i	0.814427	−	0.580266i	$-0.197052\pi$
$4$	−0.900969	−	0.433884i	−0.450484	−	0.216942i
$5$	0.623490	−	0.781831i	0.278833	−	0.349646i
$5$	0.623490	−	0.781831i	0.278833	−	0.349646i
$6$	1.33192			0.543752
$7$	−3.79472			−1.43427			−0.717135	−	0.696934i	$-0.754547\pi$
$7$	−3.79472			−1.43427			−0.717135	+	0.696934i	$0.754547\pi$
$8$	0.623490	−	0.781831i	0.220437	−	0.276419i
$9$	1.10459	−	0.531942i	0.368197	−	0.177314i
$10$	0.623490	+	0.781831i	0.197165	+	0.247237i
$11$	−2.19641	+	1.05773i	−0.662242	+	0.318919i	−0.734640	−	0.678457i	$-0.762649\pi$
$11$	−2.19641	+	1.05773i	−0.662242	+	0.318919i	0.0723985	+	0.997376i	$0.476935\pi$
$12$	−0.296379	+	1.29852i	−0.0855572	+	0.374851i
$13$	−0.277479	+	0.347948i	−0.0769588	+	0.0965033i	−0.818821	−	0.574050i	$-0.805372\pi$
$13$	−0.277479	+	0.347948i	−0.0769588	+	0.0965033i	0.741862	+	0.670553i	$0.233943\pi$
$14$	0.844405	−	3.69958i	0.225677	−	0.988755i
$15$	−1.20001	−	0.577896i	−0.309842	−	0.149212i
$16$	0.623490	+	0.781831i	0.155872	+	0.195458i
$17$	−3.59738	−	4.51097i	−0.872492	−	1.09407i	−0.994827	−	0.101581i	$-0.967610\pi$
$17$	−3.59738	−	4.51097i	−0.872492	−	1.09407i	0.122335	−	0.992489i	$-0.460962\pi$
$18$	0.272811	+	1.19526i	0.0643022	+	0.281726i
$19$	−3.07848	−	1.48252i	−0.706251	−	0.340112i	0.0460437	−	0.998939i	$-0.485339\pi$
$19$	−3.07848	−	1.48252i	−0.706251	−	0.340112i	−0.752295	+	0.658827i	$0.771053\pi$
$20$	−0.900969	+	0.433884i	−0.201463	+	0.0970194i
$21$	1.12468	+	4.92753i	0.245425	+	1.07527i
$22$	−0.542468	−	2.37671i	−0.115655	−	0.506716i
$23$	−5.17241	+	2.49090i	−1.07852	+	0.519389i	−0.886844	−	0.462069i	$-0.847107\pi$
$23$	−5.17241	+	2.49090i	−1.07852	+	0.519389i	−0.191678	+	0.981458i	$0.561393\pi$
$24$	−1.20001	−	0.577896i	−0.244952	−	0.117963i
$25$	−0.222521	−	0.974928i	−0.0445042	−	0.194986i
$26$	−0.277479	−	0.347948i	−0.0544181	−	0.0682382i
$27$	−3.50942	−	4.40068i	−0.675389	−	0.846911i
$28$	3.41893	+	1.64647i	0.646117	+	0.311153i
$29$	0.396418	−	1.73682i	0.0736129	−	0.322519i	−0.924692	−	0.380715i	$-0.875678\pi$
$29$	0.396418	−	1.73682i	0.0736129	−	0.322519i	0.998305	+	0.0581962i	$0.0185349\pi$
$30$	0.830435	−	1.04133i	0.151616	−	0.190121i
$31$	−0.394434	+	1.72813i	−0.0708424	+	0.310381i	−0.997918	−	0.0644933i	$-0.979457\pi$
$31$	−0.394434	+	1.72813i	−0.0708424	+	0.310381i	0.927076	+	0.374874i	$0.122314\pi$
$32$	−0.900969	+	0.433884i	−0.159270	+	0.0767005i
$33$	2.02446	+	2.53859i	0.352413	+	0.441912i
$34$	5.19836	−	2.50340i	0.891511	−	0.429329i
$35$	−2.36597	+	2.96683i	−0.399922	+	0.501487i
$36$	−1.22600			−0.204334
$37$	−3.78111			−0.621611			−0.310805	−	0.950474i	$-0.600599\pi$
$37$	−3.78111			−0.621611			−0.310805	+	0.950474i	$0.600599\pi$
$38$	2.13037	−	2.67140i	0.345592	−	0.433359i
$39$	0.534056	+	0.257188i	0.0855175	+	0.0411830i
$40$	−0.222521	−	0.974928i	−0.0351836	−	0.154150i
$41$	1.05623	−	4.62764i	0.164955	−	0.722715i	−0.823009	−	0.568029i	$-0.807706\pi$
$41$	1.05623	−	4.62764i	0.164955	−	0.722715i	0.987964	−	0.154686i	$-0.0494367\pi$
$42$	−5.05425			−0.779888
$43$	4.09757	−	5.11956i	0.624873	−	0.780726i
$43$	4.09757	−	5.11956i	0.624873	−	0.780726i
$44$	2.43783			0.367516
$45$	0.272811	−	1.19526i	0.0406683	−	0.178179i
$46$	−1.27748	−	5.59700i	−0.188354	−	0.825233i
$47$	3.12145	+	1.50321i	0.455311	+	0.219266i	0.647460	−	0.762100i	$-0.275831\pi$
$47$	3.12145	+	1.50321i	0.455311	+	0.219266i	−0.192149	+	0.981366i	$0.561546\pi$
$48$	0.830435	−	1.04133i	0.119863	−	0.150303i
$49$	7.39993			1.05713
$50$	1.00000			0.141421
$51$	−4.79140	+	6.00822i	−0.670930	+	0.841320i
$52$	0.400969	−	0.193096i	0.0556044	−	0.0267777i
$53$	0.499153	+	0.625919i	0.0685640	+	0.0859765i	0.814931	−	0.579558i	$-0.196775\pi$
$53$	0.499153	+	0.625919i	0.0685640	+	0.0859765i	−0.746367	+	0.665535i	$0.768203\pi$
$54$	5.07126	−	2.44219i	0.690111	−	0.332340i
$55$	−0.542468	+	2.37671i	−0.0731463	+	0.320475i
$56$	−2.36597	+	2.96683i	−0.316166	+	0.396460i
$57$	−1.01268	+	4.43685i	−0.134133	+	0.587675i
$58$	1.60506	+	0.772957i	0.210755	+	0.101494i
$59$	0.301636	+	0.378239i	0.0392696	+	0.0492425i	0.801079	−	0.598559i	$-0.204260\pi$
$59$	0.301636	+	0.378239i	0.0392696	+	0.0492425i	−0.761809	+	0.647802i	$0.775688\pi$
$60$	0.830435	+	1.04133i	0.107209	+	0.134436i
$61$	−0.824581	−	3.61273i	−0.105577	−	0.462562i	−0.999886	−	0.0151122i	$-0.995189\pi$
$61$	−0.824581	−	3.61273i	−0.105577	−	0.462562i	0.894309	−	0.447450i	$-0.147668\pi$
$62$	−1.59703	−	0.769089i	−0.202823	−	0.0976744i
$63$	−4.19161	+	2.01857i	−0.528094	+	0.254316i
$64$	−0.222521	−	0.974928i	−0.0278151	−	0.121866i
$65$	0.0990311	+	0.433884i	0.0122833	+	0.0538167i
$66$	−2.92543	+	1.40881i	−0.360095	+	0.173413i
$67$	−1.54476	−	0.743918i	−0.188723	−	0.0908840i	0.337136	−	0.941456i	$-0.390542\pi$
$67$	−1.54476	−	0.743918i	−0.188723	−	0.0908840i	−0.525859	+	0.850572i	$0.676256\pi$
$68$	1.28389	+	5.62508i	0.155694	+	0.682142i
$69$	4.76748	+	5.97823i	0.573937	+	0.719694i
$70$	−2.36597	−	2.96683i	−0.282788	−	0.354605i
$71$	10.8265	+	5.21375i	1.28487	+	0.618758i	0.946636	−	0.322305i	$-0.104458\pi$
$71$	10.8265	+	5.21375i	1.28487	+	0.618758i	0.338229	+	0.941064i	$0.390172\pi$
$72$	0.272811	−	1.19526i	0.0321511	−	0.140863i
$73$	8.88454	−	11.1409i	1.03986	−	1.30394i	0.0884237	−	0.996083i	$-0.471817\pi$
$73$	8.88454	−	11.1409i	1.03986	−	1.30394i	0.951433	−	0.307856i	$-0.0996115\pi$
$74$	0.841377	−	3.68631i	0.0978080	−	0.428525i
$75$	−1.20001	+	0.577896i	−0.138566	+	0.0667297i
$76$	2.13037	+	2.67140i	0.244370	+	0.306431i
$77$	8.33476	−	4.01381i	0.949834	−	0.457416i
$78$	−0.369579	+	0.463437i	−0.0418465	+	0.0524739i
$79$	4.26059			0.479354			0.239677	−	0.970853i	$-0.422958\pi$
$79$	4.26059			0.479354			0.239677	+	0.970853i	$0.422958\pi$
$80$	1.00000			0.111803
$81$	−2.38105	+	2.98575i	−0.264561	+	0.331749i
$82$	4.27658	+	2.05949i	0.472269	+	0.227433i
$83$	1.52492	+	6.68112i	0.167382	+	0.733348i	0.987037	+	0.160491i	$0.0513078\pi$
$83$	1.52492	+	6.68112i	0.167382	+	0.733348i	−0.819655	+	0.572857i	$0.805835\pi$
$84$	1.12468	−	4.92753i	0.122712	−	0.537637i
$85$	−5.76974			−0.625816
$86$	4.07941	+	5.13404i	0.439894	+	0.553618i
$87$	−2.37279			−0.254389
$88$	−0.542468	+	2.37671i	−0.0578273	+	0.253358i
$89$	1.95777	+	8.57754i	0.207523	+	0.909218i	0.966209	+	0.257761i	$0.0829847\pi$
$89$	1.95777	+	8.57754i	0.207523	+	0.909218i	−0.758686	+	0.651457i	$0.774158\pi$
$90$	1.10459	+	0.531942i	0.116434	+	0.0560717i
$91$	1.05296	−	1.32037i	0.110380	−	0.138412i
$92$	5.74094			0.598534
$93$	2.36091			0.244815
$94$	−2.16011	+	2.70869i	−0.222799	+	0.279381i
$95$	−3.07848	+	1.48252i	−0.315845	+	0.152103i
$96$	0.830435	+	1.04133i	0.0847560	+	0.106281i
$97$	−10.0228	+	4.82674i	−1.01766	+	0.490081i	−0.866897	−	0.498488i	$-0.833889\pi$
$97$	−10.0228	+	4.82674i	−1.01766	+	0.490081i	−0.150768	+	0.988569i	$0.548175\pi$
$98$	−1.64664	+	7.21440i	−0.166336	+	0.728764i
$99$	−1.86348	+	2.33672i	−0.187286	+	0.234850i
$100$	−0.222521	+	0.974928i	−0.0222521	+	0.0974928i
$101$	6.86776	+	3.30734i	0.683368	+	0.329093i	0.743156	−	0.669119i	$-0.233328\pi$
$101$	6.86776	+	3.30734i	0.683368	+	0.329093i	−0.0597879	+	0.998211i	$0.519042\pi$
$102$	−4.79140	−	6.00822i	−0.474419	−	0.594903i
$103$	−6.43793	−	8.07291i	−0.634349	−	0.795448i	0.355935	−	0.934511i	$-0.384162\pi$
$103$	−6.43793	−	8.07291i	−0.634349	−	0.795448i	−0.990284	+	0.139063i	$0.955591\pi$
$104$	0.0990311	+	0.433884i	0.00971080	+	0.0425458i
$105$	4.55372	+	2.19296i	0.444398	+	0.214011i
$106$	−0.721298	+	0.347359i	−0.0700586	+	0.0337385i
$107$	2.19304	+	9.60832i	0.212009	+	0.928871i	0.963200	+	0.268786i	$0.0866226\pi$
$107$	2.19304	+	9.60832i	0.212009	+	0.928871i	−0.751191	+	0.660085i	$0.770520\pi$
$108$	1.25250	+	5.48755i	0.120522	+	0.528040i
$109$	−4.33971	+	2.08990i	−0.415669	+	0.200176i	−0.630016	−	0.776582i	$-0.716952\pi$
$109$	−4.33971	+	2.08990i	−0.415669	+	0.200176i	0.214347	+	0.976758i	$0.431238\pi$
$110$	−2.19641	−	1.05773i	−0.209419	−	0.100851i
$111$	1.12064	+	4.90985i	0.106367	+	0.466023i
$112$	−2.36597	−	2.96683i	−0.223563	−	0.280340i
$113$	−6.68422	−	8.38175i	−0.628798	−	0.788488i	0.360754	−	0.932661i	$-0.382519\pi$
$113$	−6.68422	−	8.38175i	−0.628798	−	0.788488i	−0.989553	+	0.144173i	$0.953948\pi$
$114$	−4.10027	−	1.97459i	−0.384025	−	0.184937i
$115$	−1.27748	+	5.59700i	−0.119126	+	0.521923i
$116$	−1.11074	+	1.39282i	−0.103129	+	0.129320i
$117$	−0.121412	+	0.531942i	−0.0112246	+	0.0491781i
$118$	−0.435876	+	0.209907i	−0.0401256	+	0.0193235i
$119$	13.6510	+	17.1179i	1.25139	+	1.56919i
$120$	−1.20001	+	0.577896i	−0.109546	+	0.0527545i
$121$	−3.15299	+	3.95372i	−0.286635	+	0.359429i
$122$	3.70563			0.335492
$123$	−6.32213			−0.570047
$124$	1.10518	−	1.38585i	0.0992480	−	0.124453i
$125$	−0.900969	−	0.433884i	−0.0805851	−	0.0388077i
$126$	−1.03524	−	4.53570i	−0.0922268	−	0.404072i
$127$	1.36520	−	5.98132i	0.121142	−	0.530756i	−0.877544	−	0.479497i	$-0.840819\pi$
$127$	1.36520	−	5.98132i	0.121142	−	0.530756i	0.998685	−	0.0512595i	$-0.0163236\pi$
$128$	1.00000			0.0883883
$129$	−7.86230	−	3.80345i	−0.692237	−	0.334875i
$130$	−0.445042			−0.0390328
$131$	4.21827	−	18.4815i	0.368552	−	1.61473i	−0.362207	−	0.932098i	$-0.617977\pi$
$131$	4.21827	−	18.4815i	0.368552	−	1.61473i	0.730759	−	0.682635i	$-0.239166\pi$
$132$	−0.722521	−	3.16557i	−0.0628874	−	0.275528i
$133$	11.6820	+	5.62574i	1.01295	+	0.487813i
$134$	1.06901	−	1.34049i	0.0923482	−	0.115801i
$135$	−5.62868			−0.484439
$136$	−5.76974			−0.494751
$137$	−11.1112	+	13.9330i	−0.949291	+	1.19037i	0.0323189	+	0.999478i	$0.489711\pi$
$137$	−11.1112	+	13.9330i	−0.949291	+	1.19037i	−0.981610	+	0.190896i	$0.938861\pi$
$138$	−6.88921	+	3.31767i	−0.586448	+	0.282419i
$139$	−5.20108	−	6.52195i	−0.441150	−	0.553185i	0.510696	−	0.859761i	$-0.329388\pi$
$139$	−5.20108	−	6.52195i	−0.441150	−	0.553185i	−0.951846	+	0.306577i	$0.900816\pi$
$140$	3.41893	−	1.64647i	0.288952	−	0.139152i
$141$	1.02682	−	4.49879i	0.0864738	−	0.378867i
$142$	−7.49215	+	9.39486i	−0.628727	+	0.788399i
$143$	0.241421	−	1.05773i	0.0201886	−	0.0884521i
$144$	1.10459	+	0.531942i	0.0920492	+	0.0443285i
$145$	−1.11074	−	1.39282i	−0.0922417	−	0.115667i
$146$	8.88454	+	11.1409i	0.735290	+	0.922024i
$147$	−2.19318	−	9.60896i	−0.180891	−	0.792534i
$148$	3.40666	+	1.64056i	0.280026	+	0.134853i
$149$	16.8629	−	8.12072i	1.38146	−	0.665275i	0.412149	−	0.911117i	$-0.364778\pi$
$149$	16.8629	−	8.12072i	1.38146	−	0.665275i	0.969310	+	0.245841i	$0.0790642\pi$
$150$	−0.296379	−	1.29852i	−0.0241992	−	0.106024i
$151$	−3.05766	−	13.3965i	−0.248829	−	1.09019i	−0.932719	−	0.360604i	$-0.882570\pi$
$151$	−3.05766	−	13.3965i	−0.248829	−	1.09019i	0.683890	−	0.729585i	$-0.260287\pi$
$152$	−3.07848	+	1.48252i	−0.249697	+	0.120248i
$153$	−6.37320	−	3.06917i	−0.515243	−	0.248128i
$154$	2.05852	+	9.01894i	0.165880	+	0.726767i
$155$	1.10518	+	1.38585i	0.0887701	+	0.111314i
$156$	−0.369579	−	0.463437i	−0.0295900	−	0.0371046i
$157$	−19.6442	−	9.46013i	−1.56777	−	0.755000i	−0.569998	−	0.821646i	$-0.693056\pi$
$157$	−19.6442	−	9.46013i	−1.56777	−	0.755000i	−0.997777	+	0.0666460i	$0.978770\pi$
$158$	−0.948071	+	4.15377i	−0.0754245	+	0.330456i
$159$	0.664830	−	0.833671i	0.0527245	−	0.0661144i
$160$	−0.222521	+	0.974928i	−0.0175918	+	0.0770748i
$161$	19.6279	−	9.45228i	1.54689	−	0.744944i
$162$	−2.38105	−	2.98575i	−0.187073	−	0.234582i
$163$	12.7855	−	6.15715i	1.00143	−	0.482265i	0.140009	−	0.990150i	$-0.455287\pi$
$163$	12.7855	−	6.15715i	1.00143	−	0.482265i	0.861425	+	0.507885i	$0.169573\pi$
$164$	−2.95948	+	3.71108i	−0.231097	+	0.289786i
$165$	3.24698			0.252777
$166$	−6.85294			−0.531891
$167$	−6.84123	+	8.57863i	−0.529390	+	0.663834i	−0.972573	−	0.232597i	$-0.925278\pi$
$167$	−6.84123	+	8.57863i	−0.529390	+	0.663834i	0.443183	+	0.896431i	$0.353849\pi$
$168$	4.55372	+	2.19296i	0.351327	+	0.169190i
$169$	2.84870	+	12.4810i	0.219131	+	0.960074i
$170$	1.28389	−	5.62508i	0.0984698	−	0.431424i
$171$	−4.18907			−0.320346
$172$	−5.91308	+	2.83470i	−0.450868	+	0.216144i
$173$	24.1694			1.83757			0.918783	−	0.394762i	$-0.129173\pi$
$173$	24.1694			1.83757			0.918783	+	0.394762i	$0.129173\pi$
$174$	0.527995	−	2.31330i	0.0400272	−	0.175370i
$175$	0.844405	+	3.69958i	0.0638311	+	0.279662i
$176$	−2.19641	−	1.05773i	−0.165560	−	0.0797297i
$177$	0.401753	−	0.503782i	0.0301976	−	0.0378666i
$178$	−8.79813			−0.659448
$179$	−5.79883			−0.433425			−0.216713	−	0.976235i	$-0.569533\pi$
$179$	−5.79883			−0.433425			−0.216713	+	0.976235i	$0.569533\pi$
$180$	−0.764400	+	0.958527i	−0.0569750	+	0.0714444i
$181$	21.0994	−	10.1609i	1.56830	−	0.755255i	0.570486	−	0.821307i	$-0.306755\pi$
$181$	21.0994	−	10.1609i	1.56830	−	0.755255i	0.997816	+	0.0660523i	$0.0210404\pi$
$182$	1.05296	+	1.32037i	0.0780503	+	0.0978720i
$183$	−4.44681	+	2.14147i	−0.328718	+	0.158302i
$184$	−1.27748	+	5.59700i	−0.0941770	+	0.412616i
$185$	−2.35748	+	2.95619i	−0.173326	+	0.217344i
$186$	−0.525352	+	2.30172i	−0.0385207	+	0.168770i
$187$	12.6727	+	6.10285i	0.926720	+	0.446285i
$188$	−2.16011	−	2.70869i	−0.157542	−	0.197552i
$189$	13.3173	+	16.6994i	0.968690	+	1.21470i
$190$	−0.760321	−	3.33118i	−0.0551595	−	0.241669i
$191$	2.43953	+	1.17482i	0.176518	+	0.0850068i	0.520056	−	0.854132i	$-0.325911\pi$
$191$	2.43953	+	1.17482i	0.176518	+	0.0850068i	−0.343538	+	0.939139i	$0.611625\pi$
$192$	−1.20001	+	0.577896i	−0.0866036	+	0.0417061i
$193$	−4.30103	−	18.8440i	−0.309595	−	1.35642i	−0.855164	−	0.518358i	$-0.826544\pi$
$193$	−4.30103	−	18.8440i	−0.309595	−	1.35642i	0.545569	−	0.838066i	$-0.316313\pi$
$194$	−2.47544	−	10.8456i	−0.177726	−	0.778668i
$195$	0.534056	−	0.257188i	0.0382446	−	0.0184176i
$196$	−6.66710	−	3.21071i	−0.476222	−	0.229336i
$197$	0.727457	+	3.18720i	0.0518291	+	0.227078i	0.994209	−	0.107468i	$-0.0342742\pi$
$197$	0.727457	+	3.18720i	0.0518291	+	0.227078i	−0.942379	+	0.334546i	$0.891417\pi$
$198$	−1.86348	−	2.33672i	−0.132431	−	0.166064i
$199$	−6.85119	−	8.59112i	−0.485668	−	0.609008i	0.477262	−	0.878761i	$-0.341629\pi$
$199$	−6.85119	−	8.59112i	−0.485668	−	0.609008i	−0.962930	+	0.269753i	$0.913058\pi$
$200$	−0.900969	−	0.433884i	−0.0637081	−	0.0306802i
$201$	−0.508158	+	2.22639i	−0.0358427	+	0.157037i
$202$	−4.75264	+	5.95962i	−0.334394	+	0.419317i
$203$	−1.50430	+	6.59075i	−0.105581	+	0.462580i
$204$	6.92377	−	3.33431i	0.484761	−	0.233449i
$205$	−2.95948	−	3.71108i	−0.206699	−	0.259193i
$206$	9.30308	−	4.48013i	0.648177	−	0.312145i
$207$	−4.38837	+	5.50285i	−0.305013	+	0.382474i
$208$	−0.445042			−0.0308581
$209$	8.32969			0.576177
$210$	−3.15127	+	3.95157i	−0.217459	+	0.272684i
$211$	−19.3703	−	9.32823i	−1.33350	−	0.642182i	−0.374937	−	0.927050i	$-0.622336\pi$
$211$	−19.3703	−	9.32823i	−1.33350	−	0.642182i	−0.958567	+	0.284869i	$0.908050\pi$
$212$	−0.178146	−	0.780508i	−0.0122351	−	0.0536055i
$213$	3.56143	−	15.6036i	0.244025	−	1.06914i
$214$	−9.85542			−0.673702
$215$	−1.44784	−	6.39560i	−0.0987422	−	0.436177i
$216$	−5.62868			−0.382983
$217$	1.49677	−	6.55776i	0.101607	−	0.445170i
$218$	−1.07182	−	4.69595i	−0.0725929	−	0.318050i
$219$	−17.0998	−	8.23485i	−1.15550	−	0.556459i
$220$	1.51996	−	1.90597i	0.102476	−	0.128501i
$221$	2.56778			0.172727
$222$	−5.03612			−0.338002
$223$	15.4196	−	19.3356i	1.03257	−	1.29481i	0.0779622	−	0.996956i	$-0.475159\pi$
$223$	15.4196	−	19.3356i	1.03257	−	1.29481i	0.954612	−	0.297851i	$-0.0962699\pi$
$224$	3.41893	−	1.64647i	0.228437	−	0.110009i
$225$	−0.764400	−	0.958527i	−0.0509600	−	0.0639018i
$226$	9.65898	−	4.65152i	0.642506	−	0.309414i
$227$	5.91078	−	25.8968i	0.392312	−	1.71883i	−0.264157	−	0.964480i	$-0.585094\pi$
$227$	5.91078	−	25.8968i	0.392312	−	1.71883i	0.656469	−	0.754353i	$-0.272049\pi$
$228$	2.83747	−	3.55808i	0.187916	−	0.235640i
$229$	−1.20815	+	5.29323i	−0.0798365	+	0.349787i	−0.999031	−	0.0440179i	$-0.985984\pi$
$229$	−1.20815	+	5.29323i	−0.0798365	+	0.349787i	0.919194	+	0.393804i	$0.128841\pi$
$230$	−5.17241	−	2.49090i	−0.341058	−	0.164245i
$231$	−7.68226	−	9.63325i	−0.505456	−	0.633821i
$232$	−1.11074	−	1.39282i	−0.0729235	−	0.0914432i
$233$	3.29501	+	14.4364i	0.215863	+	0.945758i	0.960498	+	0.278286i	$0.0897663\pi$
$233$	3.29501	+	14.4364i	0.215863	+	0.945758i	−0.744635	+	0.667472i	$0.767377\pi$
$234$	−0.491589	−	0.236737i	−0.0321362	−	0.0154760i
$235$	3.12145	−	1.50321i	0.203621	−	0.0980588i
$236$	−0.107653	−	0.471656i	−0.00700758	−	0.0307022i
$237$	−1.26275	−	5.53247i	−0.0820244	−	0.359372i
$238$	−19.7263	+	9.49970i	−1.27867	+	0.615774i
$239$	−7.05578	−	3.39789i	−0.456401	−	0.219791i	0.191535	−	0.981486i	$-0.438653\pi$
$239$	−7.05578	−	3.39789i	−0.456401	−	0.219791i	−0.647936	+	0.761695i	$0.724368\pi$
$240$	−0.296379	−	1.29852i	−0.0191312	−	0.0838192i
$241$	−12.5523	−	15.7400i	−0.808562	−	1.01390i	−0.999478	−	0.0322980i	$-0.989717\pi$
$241$	−12.5523	−	15.7400i	−0.808562	−	1.01390i	0.190917	−	0.981606i	$-0.438854\pi$
$242$	−3.15299	−	3.95372i	−0.202682	−	0.254155i
$243$	−10.6310	−	5.11964i	−0.681981	−	0.328425i
$244$	−0.824581	+	3.61273i	−0.0527884	+	0.231281i
$245$	4.61378	−	5.78550i	0.294764	−	0.369622i
$246$	1.40681	−	6.16362i	0.0896946	−	0.392978i
$247$	1.37005	−	0.659782i	0.0871742	−	0.0419809i
$248$	1.10518	+	1.38585i	0.0701789	+	0.0880016i
$249$	8.22362	−	3.96029i	0.521151	−	0.250973i
$250$	0.623490	−	0.781831i	0.0394330	−	0.0494474i
$251$	−14.6948			−0.927528			−0.463764	−	0.885959i	$-0.653502\pi$
$251$	−14.6948			−0.927528			−0.463764	+	0.885959i	$0.653502\pi$
$252$	4.65234			0.293070
$253$	8.72600	−	10.9421i	0.548599	−	0.687921i
$254$	5.52757	+	2.66194i	0.346830	+	0.167025i
$255$	1.71003	+	7.49213i	0.107086	+	0.469176i
$256$	−0.222521	+	0.974928i	−0.0139076	+	0.0609330i
$257$	−5.32899			−0.332413			−0.166207	−	0.986091i	$-0.553152\pi$
$257$	−5.32899			−0.332413			−0.166207	+	0.986091i	$0.553152\pi$
$258$	5.45761	−	6.81882i	0.339776	−	0.424521i
$259$	14.3483			0.891558
$260$	0.0990311	−	0.433884i	0.00614165	−	0.0269083i
$261$	−0.486009	−	2.12934i	−0.0300832	−	0.131803i
$262$	17.0794	+	8.22502i	1.05517	+	0.508144i
$263$	−16.4936	+	20.6823i	−1.01704	+	1.27532i	−0.0561377	+	0.998423i	$0.517879\pi$
$263$	−16.4936	+	20.6823i	−1.01704	+	1.27532i	−0.960899	+	0.276900i	$0.910693\pi$
$264$	3.24698			0.199838
$265$	0.800580			0.0491792
$266$	−8.08417	+	10.1372i	−0.495672	+	0.621553i
$267$	10.5579	−	5.08441i	0.646132	−	0.311161i
$268$	1.06901	+	1.34049i	0.0653001	+	0.0818837i
$269$	−12.4623	+	6.00152i	−0.759838	+	0.365919i	−0.773341	−	0.633990i	$-0.781416\pi$
$269$	−12.4623	+	6.00152i	−0.759838	+	0.365919i	0.0135029	+	0.999909i	$0.495702\pi$
$270$	1.25250	−	5.48755i	0.0762246	−	0.333962i
$271$	−18.2532	+	22.8888i	−1.10880	+	1.39039i	−0.196682	+	0.980467i	$0.563017\pi$
$271$	−18.2532	+	22.8888i	−1.10880	+	1.39039i	−0.912119	+	0.409926i	$0.865555\pi$
$272$	1.28389	−	5.62508i	0.0778472	−	0.341071i
$273$	−2.02660	−	0.975958i	−0.122655	−	0.0590676i
$274$	−11.1112	−	13.9330i	−0.671250	−	0.841721i
$275$	1.51996	+	1.90597i	0.0916571	+	0.114934i
$276$	−1.70149	−	7.45473i	−0.102418	−	0.448722i
$277$	11.5964	+	5.58454i	0.696762	+	0.335543i	0.748516	−	0.663117i	$-0.230767\pi$
$277$	11.5964	+	5.58454i	0.696762	+	0.335543i	−0.0517540	+	0.998660i	$0.516481\pi$
$278$	7.51578	−	3.61941i	0.450767	−	0.217078i
$279$	0.483577	+	2.11869i	0.0289510	+	0.126843i
$280$	0.844405	+	3.69958i	0.0504629	+	0.221092i
$281$	−15.1747	+	7.30775i	−0.905247	+	0.435944i	−0.827781	−	0.561051i	$-0.810397\pi$
$281$	−15.1747	+	7.30775i	−0.905247	+	0.435944i	−0.0774659	+	0.996995i	$0.524683\pi$
$282$	4.15751	+	2.00215i	0.247576	+	0.119226i
$283$	−3.00840	−	13.1807i	−0.178831	−	0.783509i	−0.982171	−	0.187989i	$-0.939803\pi$
$283$	−3.00840	−	13.1807i	−0.178831	−	0.783509i	0.803340	−	0.595520i	$-0.203054\pi$
$284$	−7.49215	−	9.39486i	−0.444577	−	0.557482i
$285$	2.83747	+	3.55808i	0.168077	+	0.210762i
$286$	0.977493	+	0.470736i	0.0578004	+	0.0278352i
$287$	−4.00809	+	17.5606i	−0.236590	+	1.03657i
$288$	−0.764400	+	0.958527i	−0.0450427	+	0.0564818i
$289$	−3.62485	+	15.8815i	−0.213227	+	0.934206i
$290$	1.60506	−	0.772957i	0.0942525	−	0.0453896i
$291$	9.23818	+	11.5843i	0.541552	+	0.679085i
$292$	−12.8385	+	6.18271i	−0.751318	+	0.361816i
$293$	−8.61875	+	10.8076i	−0.503513	+	0.631385i	−0.967018	−	0.254709i	$-0.918020\pi$
$293$	−8.61875	+	10.8076i	−0.503513	+	0.631385i	0.463505	+	0.886094i	$0.346592\pi$
$294$	9.85608			0.574818
$295$	0.483786			0.0281671
$296$	−2.35748	+	2.95619i	−0.137026	+	0.171825i
$297$	12.3629	+	5.95364i	0.717366	+	0.345465i
$298$	4.16478	+	18.2471i	0.241259	+	1.05703i
$299$	0.568532	−	2.49090i	0.0328790	−	0.144052i
$300$	1.33192			0.0768982
$301$	−15.5491	+	19.4273i	−0.896237	+	1.11977i
$302$	13.7410			0.790705
$303$	2.25919	−	9.89816i	0.129787	−	0.568634i
$304$	−0.760321	−	3.33118i	−0.0436074	−	0.191056i
$305$	−3.33866	−	1.60781i	−0.191171	−	0.0920632i
$306$	4.41039	−	5.53046i	0.252125	−	0.316155i
$307$	20.3288			1.16023			0.580114	−	0.814536i	$-0.303008\pi$
$307$	20.3288			1.16023			0.580114	+	0.814536i	$0.303008\pi$
$308$	−9.25088			−0.527118
$309$	−8.57478	+	10.7524i	−0.487802	+	0.611685i
$310$	−1.59703	+	0.769089i	−0.0907052	+	0.0436813i
$311$	−16.6026	−	20.8190i	−0.941447	−	1.18054i	−0.983406	−	0.181417i	$-0.941932\pi$
$311$	−16.6026	−	20.8190i	−0.941447	−	1.18054i	0.0419597	−	0.999119i	$-0.486640\pi$
$312$	0.534056	−	0.257188i	0.0302350	−	0.0145604i
$313$	−3.65013	+	15.9923i	−0.206318	+	0.903937i	0.760675	+	0.649133i	$0.224868\pi$
$313$	−3.65013	+	15.9923i	−0.206318	+	0.903937i	−0.966993	+	0.254804i	$0.917989\pi$
$314$	13.5942	−	17.0466i	0.767164	−	0.961993i
$315$	−1.03524	+	4.53570i	−0.0583293	+	0.255558i
$316$	−3.83866	−	1.84860i	−0.215942	−	0.103992i
$317$	15.5192	+	19.4605i	0.871647	+	1.09301i	0.994923	+	0.100638i	$0.0320885\pi$
$317$	15.5192	+	19.4605i	0.871647	+	1.09301i	−0.123276	+	0.992372i	$0.539340\pi$
$318$	0.664830	+	0.833671i	0.0372818	+	0.0467499i
$319$	0.966398	+	4.23407i	0.0541079	+	0.237062i
$320$	−0.900969	−	0.433884i	−0.0503657	−	0.0242548i
$321$	11.8266	−	5.69541i	0.660099	−	0.317887i
$322$	4.84768	+	21.2391i	0.270151	+	1.18361i
$323$	4.38686	+	19.2201i	0.244091	+	1.06943i
$324$	3.44072	−	1.65696i	0.191151	−	0.0920535i
$325$	0.400969	+	0.193096i	0.0222418	+	0.0107111i
$326$	3.15775	+	13.8350i	0.174891	+	0.766249i
$327$	3.99997	+	5.01581i	0.221199	+	0.277375i
$328$	−2.95948	−	3.71108i	−0.163410	−	0.204910i
$329$	−11.8450	−	5.70428i	−0.653039	−	0.314487i
$330$	−0.722521	+	3.16557i	−0.0397735	+	0.174259i
$331$	3.04607	−	3.81965i	0.167427	−	0.209947i	−0.691039	−	0.722818i	$-0.742847\pi$
$331$	3.04607	−	3.81965i	0.167427	−	0.209947i	0.858466	+	0.512871i	$0.171418\pi$
$332$	1.52492	−	6.68112i	0.0836910	−	0.366674i
$333$	−4.17658	+	2.01133i	−0.228875	+	0.110220i
$334$	−6.84123	−	8.57863i	−0.374335	−	0.469402i
$335$	−1.54476	+	0.743918i	−0.0843993	+	0.0406446i
$336$	−3.15127	+	3.95157i	−0.171916	+	0.215576i
$337$	3.13131			0.170573			0.0852866	−	0.996356i	$-0.472819\pi$
$337$	3.13131			0.170573			0.0852866	+	0.996356i	$0.472819\pi$
$338$	−12.8019			−0.696334
$339$	−8.90281	+	11.1638i	−0.483534	+	0.606333i
$340$	5.19836	+	2.50340i	0.281921	+	0.135766i
$341$	−0.961561	−	4.21288i	−0.0520715	−	0.228140i
$342$	0.932155	−	4.08404i	0.0504052	−	0.220839i
$343$	−1.51762			−0.0819436
$344$	−1.44784	−	6.39560i	−0.0780625	−	0.344828i
$345$	7.64644			0.411671
$346$	−5.37820	+	23.5634i	−0.289134	+	1.26678i
$347$	−4.54240	−	19.9016i	−0.243849	−	1.06837i	−0.937479	−	0.348041i	$-0.886847\pi$
$347$	−4.54240	−	19.9016i	−0.243849	−	1.06837i	0.693630	−	0.720331i	$-0.256010\pi$
$348$	2.13781	+	1.02951i	0.114598	+	0.0551877i
$349$	−17.4963	+	21.9397i	−0.936556	+	1.17440i	0.0479141	+	0.998851i	$0.484743\pi$
$349$	−17.4963	+	21.9397i	−0.936556	+	1.17440i	−0.984470	+	0.175553i	$0.943829\pi$
$350$	−3.79472			−0.202837
$351$	2.50500			0.133707
$352$	1.51996	−	1.90597i	0.0810142	−	0.101589i
$353$	21.3636	−	10.2882i	1.13707	−	0.547585i	0.231946	−	0.972729i	$-0.425491\pi$
$353$	21.3636	−	10.2882i	1.13707	−	0.547585i	0.905126	+	0.425144i	$0.139776\pi$
$354$	0.401753	+	0.503782i	0.0213529	+	0.0267757i
$355$	10.8265	−	5.21375i	0.574609	−	0.276717i
$356$	1.95777	−	8.57754i	0.103761	−	0.454609i
$357$	18.1820	−	22.7996i	0.962295	−	1.20668i
$358$	1.29036	−	5.65345i	0.0681977	−	0.298794i
$359$	−14.3948	−	6.93215i	−0.759726	−	0.365865i	0.0135717	−	0.999908i	$-0.495680\pi$
$359$	−14.3948	−	6.93215i	−0.759726	−	0.365865i	−0.773298	+	0.634043i	$0.781394\pi$
$360$	−0.764400	−	0.958527i	−0.0402874	−	0.0505188i
$361$	−4.56715	−	5.72702i	−0.240376	−	0.301422i
$362$	5.21111	+	22.8314i	0.273890	+	1.19999i
$363$	6.06847	+	2.92242i	0.318512	+	0.153387i
$364$	−1.52157	+	0.732748i	−0.0797517	+	0.0384064i
$365$	−3.17086	−	13.8924i	−0.165970	−	0.727163i
$366$	−1.09827	−	4.81184i	−0.0574076	−	0.251519i
$367$	−24.4427	+	11.7710i	−1.27590	+	0.614440i	−0.944333	−	0.328992i	$-0.893291\pi$
$367$	−24.4427	+	11.7710i	−1.27590	+	0.614440i	−0.331566	+	0.943432i	$0.607577\pi$
$368$	−5.17241	−	2.49090i	−0.269630	−	0.129847i
$369$	−1.29494	−	5.67349i	−0.0674118	−	0.295350i
$370$	−2.35748	−	2.95619i	−0.122560	−	0.153685i
$371$	−1.89415	−	2.37519i	−0.0983393	−	0.123314i
$372$	−2.12711	−	1.02436i	−0.110285	−	0.0531106i
$373$	−6.40023	+	28.0412i	−0.331391	+	1.45192i	0.485047	+	0.874488i	$0.338802\pi$
$373$	−6.40023	+	28.0412i	−0.331391	+	1.45192i	−0.816439	+	0.577432i	$0.804055\pi$
$374$	−8.76978	+	10.9970i	−0.453475	+	0.568639i
$375$	−0.296379	+	1.29852i	−0.0153049	+	0.0670553i
$376$	3.12145	−	1.50321i	0.160977	−	0.0775223i
$377$	0.494325	+	0.619863i	0.0254590	+	0.0319246i
$378$	−19.2440	+	9.26744i	−0.989806	+	0.476666i
$379$	0.764118	−	0.958173i	0.0392501	−	0.0492180i	−0.761819	−	0.647790i	$-0.775693\pi$
$379$	0.764118	−	0.958173i	0.0392501	−	0.0492180i	0.801069	+	0.598572i	$0.204265\pi$
$380$	3.41685			0.175281
$381$	−8.17148			−0.418638
$382$	−1.68821	+	2.11695i	−0.0863763	+	0.108312i
$383$	26.2116	+	12.6228i	1.33935	+	0.644997i	0.959933	−	0.280228i	$-0.0904101\pi$
$383$	26.2116	+	12.6228i	1.33935	+	0.644997i	0.379418	+	0.925226i	$0.376124\pi$
$384$	−0.296379	−	1.29852i	−0.0151245	−	0.0662649i
$385$	2.05852	−	9.01894i	0.104912	−	0.459648i
$386$	19.3286			0.983802
$387$	1.80282	−	7.83469i	0.0916424	−	0.398260i
$388$	11.1245			0.564761
$389$	−1.78472	+	7.81935i	−0.0904887	+	0.396457i	−0.999807	−	0.0196443i	$-0.993747\pi$
$389$	−1.78472	+	7.81935i	−0.0904887	+	0.396457i	0.909318	+	0.416101i	$0.136604\pi$
$390$	0.131901	+	0.577896i	0.00667907	+	0.0292629i
$391$	29.8435	+	14.3719i	1.50925	+	0.726816i
$392$	4.61378	−	5.78550i	0.233031	−	0.292212i
$393$	−25.2488			−1.27363
$394$	−3.26916			−0.164698
$395$	2.65644	−	3.33106i	0.133660	−	0.167604i
$396$	2.69280	−	1.29678i	0.135318	−	0.0651659i
$397$	2.24327	+	2.81297i	0.112586	+	0.141179i	0.834931	−	0.550354i	$-0.185507\pi$
$397$	2.24327	+	2.81297i	0.112586	+	0.141179i	−0.722345	+	0.691533i	$0.756936\pi$
$398$	9.90025	−	4.76771i	0.496255	−	0.238984i
$399$	3.84285	−	16.8366i	0.192383	−	0.842886i
$400$	0.623490	−	0.781831i	0.0311745	−	0.0390916i
$401$	0.843332	−	3.69488i	0.0421140	−	0.184513i	−0.949496	−	0.313779i	$-0.898405\pi$
$401$	0.843332	−	3.69488i	0.0421140	−	0.184513i	0.991610	+	0.129266i	$0.0412620\pi$
$402$	−2.05749	−	0.990835i	−0.102618	−	0.0494184i
$403$	−0.491851	−	0.616761i	−0.0245008	−	0.0307231i
$404$	−4.75264	−	5.95962i	−0.236453	−	0.296502i
$405$	0.849788	+	3.72316i	0.0422263	+	0.185005i
$406$	−6.09077	−	2.93316i	−0.302280	−	0.145570i
$407$	8.30486	−	3.99941i	0.411657	−	0.198243i
$408$	1.71003	+	7.49213i	0.0846591	+	0.370916i
$409$	−1.30925	−	5.73619i	−0.0647382	−	0.283636i	0.932189	−	0.361972i	$-0.117897\pi$
$409$	−1.30925	−	5.73619i	−0.0647382	−	0.283636i	−0.996927	+	0.0783358i	$0.975039\pi$
$410$	4.27658	−	2.05949i	0.211205	−	0.101711i
$411$	21.3854	+	10.2987i	1.05486	+	0.507995i
$412$	2.29767	+	10.0668i	0.113198	+	0.495954i
$413$	−1.14462	−	1.43531i	−0.0563233	−	0.0706271i
$414$	−4.38837	−	5.50285i	−0.215677	−	0.270450i
$415$	6.17428	+	2.97338i	0.303084	+	0.145957i
$416$	0.0990311	−	0.433884i	0.00485540	−	0.0212729i
$417$	−6.92740	+	8.68668i	−0.339236	+	0.425389i
$418$	−1.85353	+	8.12085i	−0.0906592	+	0.397204i
$419$	−5.03200	+	2.42328i	−0.245829	+	0.118385i	−0.552742	−	0.833353i	$-0.686418\pi$
$419$	−5.03200	+	2.42328i	−0.245829	+	0.118385i	0.306912	+	0.951738i	$0.400704\pi$
$420$	−3.15127	−	3.95157i	−0.153766	−	0.192817i
$421$	24.5336	−	11.8148i	1.19570	−	0.575817i	0.273250	−	0.961943i	$-0.411901\pi$
$421$	24.5336	−	11.8148i	1.19570	−	0.575817i	0.922446	+	0.386126i	$0.126187\pi$
$422$	13.4046	−	16.8089i	0.652527	−	0.818244i
$423$	4.24755			0.206523
$424$	0.800580			0.0388796
$425$	−3.59738	+	4.51097i	−0.174498	+	0.218814i
$426$	14.4199	+	6.94427i	0.698648	+	0.336451i
$427$	3.12906	+	13.7093i	0.151426	+	0.663439i
$428$	2.19304	−	9.60832i	0.106004	−	0.464436i
$429$	−1.44504			−0.0697673
$430$	6.55743	+	0.0116118i	0.316227	+	0.000559972i
$431$	−12.0151			−0.578748			−0.289374	−	0.957216i	$-0.593447\pi$
$431$	−12.0151			−0.578748			−0.289374	+	0.957216i	$0.593447\pi$
$432$	1.25250	−	5.48755i	0.0602609	−	0.264020i
$433$	0.968456	+	4.24308i	0.0465410	+	0.203910i	0.992853	−	0.119346i	$-0.0380798\pi$
$433$	0.968456	+	4.24308i	0.0465410	+	0.203910i	−0.946312	+	0.323256i	$0.895223\pi$
$434$	6.06029	+	2.91848i	0.290903	+	0.140092i
$435$	−1.47941	+	1.85512i	−0.0709322	+	0.0889461i
$436$	4.81672			0.230679
$437$	19.6159			0.938357
$438$	11.8335	−	14.8387i	0.565424	−	0.709019i
$439$	28.6086	−	13.7772i	1.36542	−	0.657549i	0.399578	−	0.916699i	$-0.369157\pi$
$439$	28.6086	−	13.7772i	1.36542	−	0.657549i	0.965837	+	0.259150i	$0.0834423\pi$
$440$	1.51996	+	1.90597i	0.0724613	+	0.0908636i
$441$	8.17389	−	3.93634i	0.389233	−	0.187445i
$442$	−0.571384	+	2.50340i	−0.0271780	+	0.119074i
$443$	−10.9360	+	13.7133i	−0.519585	+	0.651538i	−0.970521	−	0.241018i	$-0.922519\pi$
$443$	−10.9360	+	13.7133i	−0.519585	+	0.651538i	0.450936	+	0.892556i	$0.351090\pi$
$444$	1.12064	−	4.90985i	0.0531833	−	0.233011i
$445$	7.92684	+	3.81737i	0.375768	+	0.180960i
$446$	15.4196	+	19.3356i	0.730140	+	0.915567i
$447$	−15.5427	−	19.4900i	−0.735146	−	0.921843i
$448$	0.844405	+	3.69958i	0.0398944	+	0.174789i
$449$	−17.7778	−	8.56132i	−0.838984	−	0.404033i	−0.0355073	−	0.999369i	$-0.511305\pi$
$449$	−17.7778	−	8.56132i	−0.838984	−	0.404033i	−0.803477	+	0.595336i	$0.797019\pi$
$450$	1.10459	−	0.531942i	0.0520709	−	0.0250760i
$451$	2.57490	+	11.2814i	0.121247	+	0.531219i
$452$	2.38557	+	10.4519i	0.112208	+	0.491614i
$453$	−16.4894	+	7.94087i	−0.774738	+	0.373094i
$454$	23.9323	+	11.5252i	1.12320	+	0.540903i
$455$	−0.375796	−	1.64647i	−0.0176176	−	0.0771877i
$456$	2.83747	+	3.55808i	0.132877	+	0.166622i
$457$	−7.51414	−	9.42244i	−0.351497	−	0.440763i	0.574380	−	0.818589i	$-0.305243\pi$
$457$	−7.51414	−	9.42244i	−0.351497	−	0.440763i	−0.925877	+	0.377826i	$0.876672\pi$
$458$	−4.89168	−	2.35571i	−0.228573	−	0.110075i
$459$	−7.22659	+	31.6618i	−0.337308	+	1.47784i
$460$	3.57942	−	4.48845i	0.166891	−	0.209275i
$461$	1.58694	−	6.95286i	0.0739114	−	0.323827i	−0.924433	−	0.381344i	$-0.875461\pi$
$461$	1.58694	−	6.95286i	0.0739114	−	0.323827i	0.998345	+	0.0575173i	$0.0183184\pi$
$462$	11.1012	−	5.34605i	0.516474	−	0.248721i
$463$	−24.5483	−	30.7826i	−1.14086	−	1.43059i	−0.886047	−	0.463595i	$-0.846559\pi$
$463$	−24.5483	−	30.7826i	−1.14086	−	1.43059i	−0.254808	−	0.966992i	$-0.582012\pi$
$464$	1.60506	−	0.772957i	0.0745131	−	0.0358836i
$465$	1.47200	−	1.84583i	0.0682626	−	0.0855985i
$466$	−14.8076			−0.685950
$467$	32.5232			1.50500			0.752498	−	0.658595i	$-0.228849\pi$
$467$	32.5232			1.50500			0.752498	+	0.658595i	$0.228849\pi$
$468$	0.340190	−	0.426585i	0.0157253	−	0.0197189i
$469$	5.86194	+	2.82296i	0.270679	+	0.130352i
$470$	0.770935	+	3.37769i	0.0355606	+	0.155801i
$471$	−6.46206	+	28.3121i	−0.297756	+	1.30455i
$472$	0.483786			0.0222681
$473$	−3.58479	+	15.5788i	−0.164829	+	0.716313i
$474$	5.67475			0.260650
$475$	−0.760321	+	3.33118i	−0.0348859	+	0.152845i
$476$	−4.87200	−	21.3456i	−0.223308	−	0.978376i
$477$	0.884313	+	0.425863i	0.0404899	+	0.0194989i
$478$	4.88275	−	6.12278i	0.223332	−	0.280049i
$479$	4.37268			0.199793			0.0998965	−	0.994998i	$-0.468149\pi$
$479$	4.37268			0.199793			0.0998965	+	0.994998i	$0.468149\pi$
$480$	1.33192			0.0607933
$481$	1.04918	−	1.31563i	0.0478385	−	0.0599875i
$482$	18.1385	−	8.73506i	0.826187	−	0.397871i
$483$	−18.0913	−	22.6857i	−0.823181	−	1.03224i
$484$	4.55620	−	2.19415i	0.207100	−	0.0997340i
$485$	−2.47544	+	10.8456i	−0.112404	+	0.492473i
$486$	7.35691	−	9.22527i	0.333716	−	0.418467i
$487$	−4.39259	+	19.2452i	−0.199047	+	0.872082i	0.772458	+	0.635065i	$0.219027\pi$
$487$	−4.39259	+	19.2452i	−0.199047	+	0.872082i	−0.971506	+	0.237017i	$0.923830\pi$
$488$	−3.33866	−	1.60781i	−0.151134	−	0.0727823i
$489$	−11.7845	−	14.7773i	−0.532915	−	0.668254i
$490$	4.61378	+	5.78550i	0.208429	+	0.261362i
$491$	4.95161	+	21.6944i	0.223463	+	0.979056i	0.954849	+	0.297092i	$0.0960168\pi$
$491$	4.95161	+	21.6944i	0.223463	+	0.979056i	−0.731386	+	0.681964i	$0.761126\pi$
$492$	5.69604	+	2.74307i	0.256797	+	0.123667i
$493$	−9.26080	+	4.45976i	−0.417085	+	0.200858i
$494$	0.338375	+	1.48252i	0.0152242	+	0.0667015i
$495$	0.665067	+	2.91385i	0.0298925	+	0.130968i
$496$	−1.59703	+	0.769089i	−0.0717087	+	0.0345331i
$497$	−41.0834	−	19.7847i	−1.84284	−	0.887467i
$498$	2.03107	+	8.89868i	0.0910143	+	0.398760i
$499$	−16.6455	−	20.8728i	−0.745154	−	0.934394i	0.254310	−	0.967123i	$-0.418152\pi$
$499$	−16.6455	−	20.8728i	−0.745154	−	0.934394i	−0.999464	+	0.0327292i	$0.989580\pi$
$500$	0.623490	+	0.781831i	0.0278833	+	0.0349646i
$501$	13.1671	+	6.34095i	0.588264	+	0.283293i
$502$	3.26990	−	14.3264i	0.145943	−	0.639418i
$503$	10.6168	−	13.3130i	0.473378	−	0.593597i	−0.486617	−	0.873616i	$-0.661769\pi$
$503$	10.6168	−	13.3130i	0.473378	−	0.593597i	0.959995	+	0.280018i	$0.0903405\pi$
$504$	−1.03524	+	4.53570i	−0.0461134	+	0.202036i
$505$	6.86776	−	3.30734i	0.305611	−	0.147175i
$506$	8.72600	+	10.9421i	0.387918	+	0.486434i
$507$	15.3625	−	7.39819i	0.682273	−	0.328565i
$508$	−3.82520	+	4.79664i	−0.169716	+	0.212817i
$509$	−11.2032			−0.496574			−0.248287	−	0.968686i	$-0.579868\pi$
$509$	−11.2032			−0.496574			−0.248287	+	0.968686i	$0.579868\pi$
$510$	−7.68481			−0.340289
$511$	−33.7144	+	42.2765i	−1.49144	+	1.87020i
$512$	−0.900969	−	0.433884i	−0.0398176	−	0.0191751i
$513$	4.27960	+	18.7501i	0.188949	+	0.827839i
$514$	1.18581	−	5.19538i	0.0523039	−	0.229158i
$515$	−10.3256			−0.455002
$516$	5.43343	+	6.83811i	0.239193	+	0.301031i
$517$	−8.44598			−0.371454
$518$	−3.19279	+	13.9885i	−0.140283	+	0.614621i
$519$	−7.16331	−	31.3845i	−0.314434	−	1.37763i
$520$	0.400969	+	0.193096i	0.0175836	+	0.00846784i
$521$	11.8091	−	14.8081i	0.517365	−	0.648756i	−0.452682	−	0.891672i	$-0.649533\pi$
$521$	11.8091	−	14.8081i	0.517365	−	0.648756i	0.970047	+	0.242917i	$0.0781041\pi$
$522$	2.18410			0.0955956
$523$	44.5686			1.94885			0.974424	−	0.224718i	$-0.0721460\pi$
$523$	44.5686			1.94885			0.974424	+	0.224718i	$0.0721460\pi$
$524$	−11.8193	+	14.8210i	−0.516330	+	0.647458i
$525$	4.55372	−	2.19296i	0.198741	−	0.0957085i
$526$	−16.4936	−	20.6823i	−0.719153	−	0.901790i
$527$	9.21445	−	4.43744i	0.401388	−	0.193298i
$528$	−0.722521	+	3.16557i	−0.0314437	+	0.137764i
$529$	6.20895	−	7.78577i	0.269954	−	0.338512i
$530$	−0.178146	+	0.780508i	−0.00773816	+	0.0339031i
$531$	0.534385	+	0.257346i	0.0231903	+	0.0111679i
$532$	−8.08417	−	10.1372i	−0.350493	−	0.439505i
$533$	1.31709	+	1.65158i	0.0570497	+	0.0715380i
$534$	2.60758	+	11.4246i	0.112841	+	0.494389i
$535$	8.87942	+	4.27610i	0.383891	+	0.184872i
$536$	−1.54476	+	0.743918i	−0.0667235	+	0.0321324i
$537$	1.71865	+	7.52991i	0.0741653	+	0.324940i
$538$	−3.07793	−	13.4853i	−0.132699	−	0.581392i
$539$	−16.2533	+	7.82715i	−0.700077	+	0.337139i
$540$	5.07126	+	2.44219i	0.218232	+	0.105095i
$541$	−4.30647	−	18.8679i	−0.185150	−	0.811193i	−0.979128	−	0.203247i	$-0.934851\pi$
$541$	−4.30647	−	18.8679i	−0.185150	−	0.811193i	0.793978	−	0.607947i	$-0.208007\pi$
$542$	−18.2532	−	22.8888i	−0.784041	−	0.983156i
$543$	−19.4476	−	24.3865i	−0.834575	−	1.04652i
$544$	5.19836	+	2.50340i	0.222878	+	0.107332i
$545$	−1.07182	+	4.69595i	−0.0459118	+	0.201153i
$546$	1.40245	−	1.75861i	0.0600193	−	0.0752618i
$547$	0.808919	−	3.54411i	0.0345869	−	0.151535i	−0.954686	−	0.297615i	$-0.903809\pi$
$547$	0.808919	−	3.54411i	0.0345869	−	0.151535i	0.989273	+	0.146080i	$0.0466658\pi$
$548$	16.0561	−	7.73221i	0.685883	−	0.330304i
$549$	−2.83259	−	3.55195i	−0.120892	−	0.151594i
$550$	−2.19641	+	1.05773i	−0.0936551	+	0.0451019i
$551$	−3.79522	+	4.75906i	−0.161682	+	0.202743i
$552$	7.64644			0.325454
$553$	−16.1678			−0.687523
$554$	−8.02497	+	10.0630i	−0.340949	+	0.427536i
$555$	4.53739	+	2.18509i	0.192601	+	0.0927519i
$556$	1.85624	+	8.13274i	0.0787223	+	0.344905i
$557$	−9.87351	+	43.2587i	−0.418354	+	1.83293i	0.123355	+	0.992363i	$0.460634\pi$
$557$	−9.87351	+	43.2587i	−0.418354	+	1.83293i	−0.541709	+	0.840566i	$0.682223\pi$
$558$	−2.17317			−0.0919978
$559$	0.644351	+	2.84631i	0.0272532	+	0.120386i
$560$	−3.79472			−0.160356
$561$	4.16876	−	18.2645i	0.176005	−	0.771129i
$562$	−3.74784	−	16.4204i	−0.158093	−	0.692652i
$563$	0.360186	+	0.173457i	0.0151800	+	0.00731032i	0.441458	−	0.897282i	$-0.354461\pi$
$563$	0.360186	+	0.173457i	0.0151800	+	0.00731032i	−0.426278	+	0.904592i	$0.640176\pi$
$564$	−2.87709	+	3.60775i	−0.121147	+	0.151914i
$565$	−10.7207			−0.451021
$566$	13.5196			0.568272
$567$	9.03544	−	11.3301i	0.379453	−	0.475819i
$568$	10.8265	−	5.21375i	0.454268	−	0.218764i
$569$	−25.2357	−	31.6446i	−1.05794	−	1.32661i	−0.942837	−	0.333255i	$-0.891853\pi$
$569$	−25.2357	−	31.6446i	−1.05794	−	1.32661i	−0.115099	−	0.993354i	$-0.536718\pi$
$570$	−4.10027	+	1.97459i	−0.171741	+	0.0827063i
$571$	−3.46094	+	15.1634i	−0.144836	+	0.634567i	0.849437	+	0.527691i	$0.176942\pi$
$571$	−3.46094	+	15.1634i	−0.144836	+	0.634567i	−0.994272	+	0.106876i	$0.965915\pi$
$572$	−0.676446	+	0.848237i	−0.0282836	+	0.0354666i
$573$	0.802499	−	3.51598i	0.0335249	−	0.146882i
$574$	−16.2284	−	7.81520i	−0.677362	−	0.326200i
$575$	3.57942	+	4.48845i	0.149272	+	0.187181i
$576$	−0.764400	−	0.958527i	−0.0318500	−	0.0399386i
$577$	−4.14329	−	18.1529i	−0.172487	−	0.755717i	−0.984969	−	0.172730i	$-0.944741\pi$
$577$	−4.14329	−	18.1529i	−0.172487	−	0.755717i	0.812482	−	0.582987i	$-0.198116\pi$
$578$	−14.6767	−	7.06794i	−0.610471	−	0.293987i
$579$	−23.1946	+	11.1700i	−0.963936	+	0.464207i
$580$	0.396418	+	1.73682i	0.0164603	+	0.0721175i
$581$	−5.78666	−	25.3530i	−0.240071	−	1.05182i
$582$	−13.3496	+	6.42881i	−0.553357	+	0.266483i
$583$	−1.75840	−	0.846801i	−0.0728255	−	0.0350709i
$584$	−3.17086	−	13.8924i	−0.131211	−	0.574873i
$585$	0.340190	+	0.426585i	0.0140651	+	0.0176371i
$586$	−8.61875	−	10.8076i	−0.356037	−	0.446456i
$587$	41.5208	+	19.9954i	1.71375	+	0.825297i	0.990949	+	0.134238i	$0.0428587\pi$
$587$	41.5208	+	19.9954i	1.71375	+	0.825297i	0.722798	+	0.691059i	$0.242856\pi$
$588$	−2.19318	+	9.60896i	−0.0904453	+	0.396267i
$589$	3.77623	−	4.73524i	0.155597	−	0.195112i
$590$	−0.107653	+	0.471656i	−0.00443198	+	0.0194178i
$591$	3.92304	−	1.88924i	0.161372	−	0.0777128i
$592$	−2.35748	−	2.95619i	−0.0968920	−	0.121499i
$593$	−39.3619	+	18.9557i	−1.61640	+	0.778416i	−0.999960	−	0.00898632i	$-0.997140\pi$
$593$	−39.3619	+	18.9557i	−1.61640	+	0.778416i	−0.616439	+	0.787403i	$0.711425\pi$
$594$	−8.55537	+	10.7281i	−0.351031	+	0.440179i
$595$	21.8946			0.897590
$596$	−18.7164			−0.766652
$597$	−9.12520	+	11.4426i	−0.373469	+	0.468316i
$598$	2.30194	+	1.10855i	0.0941332	+	0.0453322i
$599$	4.78733	+	20.9747i	0.195605	+	0.857001i	0.973515	+	0.228625i	$0.0734230\pi$
$599$	4.78733	+	20.9747i	0.195605	+	0.857001i	−0.777910	+	0.628376i	$0.783720\pi$
$600$	−0.296379	+	1.29852i	−0.0120996	+	0.0530119i
$601$	−34.2335			−1.39641			−0.698207	−	0.715896i	$-0.746018\pi$
$601$	−34.2335			−1.39641			−0.698207	+	0.715896i	$0.746018\pi$
$602$	−15.4802	−	19.4823i	−0.630927	−	0.794038i
$603$	−2.10205			−0.0856021
$604$	−3.05766	+	13.3965i	−0.124414	+	0.545095i
$605$	1.12529	+	4.93021i	0.0457494	+	0.200441i
$606$	9.14727	+	4.40510i	0.371583	+	0.178945i
$607$	6.69584	−	8.39631i	0.271776	−	0.340796i	−0.627149	−	0.778899i	$-0.715778\pi$
$607$	6.69584	−	8.39631i	0.271776	−	0.340796i	0.898924	+	0.438104i	$0.144350\pi$
$608$	3.41685			0.138572
$609$	9.00407			0.364863
$610$	2.31042	−	2.89718i	0.0935464	−	0.117303i
$611$	−1.38918	+	0.668992i	−0.0562001	+	0.0270645i
$612$	4.41039	+	5.53046i	0.178279	+	0.223555i
$613$	15.8801	−	7.64747i	0.641393	−	0.308878i	−0.0847708	−	0.996400i	$-0.527016\pi$
$613$	15.8801	−	7.64747i	0.641393	−	0.308878i	0.726164	+	0.687522i	$0.241302\pi$
$614$	−4.52359	+	19.8191i	−0.182557	+	0.799835i
$615$	−3.94178	+	4.94284i	−0.158948	+	0.199314i
$616$	2.05852	−	9.01894i	0.0829399	−	0.363384i
$617$	4.01588	+	1.93395i	0.161673	+	0.0778578i	0.512970	−	0.858406i	$-0.328545\pi$
$617$	4.01588	+	1.93395i	0.161673	+	0.0778578i	−0.351297	+	0.936264i	$0.614259\pi$
$618$	−8.57478	−	10.7524i	−0.344928	−	0.432526i
$619$	10.7125	+	13.4331i	0.430572	+	0.539920i	0.949031	−	0.315182i	$-0.102066\pi$
$619$	10.7125	+	13.4331i	0.430572	+	0.539920i	−0.518459	+	0.855102i	$0.673494\pi$
$620$	−0.394434	−	1.72813i	−0.0158408	−	0.0694032i
$621$	29.1138	+	14.0205i	1.16830	+	0.562622i
$622$	23.9914	−	11.5537i	0.961969	−	0.463260i
$623$	−7.42919	−	32.5494i	−0.297644	−	1.30406i
$624$	0.131901	+	0.577896i	0.00528027	+	0.0231344i
$625$	−0.900969	+	0.433884i	−0.0360388	+	0.0173553i
$626$	−14.7791	−	7.11723i	−0.590691	−	0.284462i
$627$	−2.46875	−	10.8163i	−0.0985922	−	0.431961i
$628$	13.5942	+	17.0466i	0.542467	+	0.680232i
$629$	13.6021	+	17.0565i	0.542350	+	0.680086i
$630$	−4.19161	−	2.01857i	−0.166998	−	0.0804219i
$631$	−1.20540	+	5.28121i	−0.0479862	+	0.210241i	−0.993237	−	0.116103i	$-0.962960\pi$
$631$	−1.20540	+	5.28121i	−0.0479862	+	0.210241i	0.945251	+	0.326344i	$0.105817\pi$
$632$	2.65644	−	3.33106i	0.105667	−	0.132503i
$633$	−6.37196	+	27.9174i	−0.253263	+	1.10962i
$634$	−22.4259	+	10.7998i	−0.890648	+	0.428913i
$635$	−3.82520	−	4.79664i	−0.151798	−	0.190349i
$636$	−0.960707	+	0.462652i	−0.0380945	+	0.0183454i
$637$	−2.05333	+	2.57479i	−0.0813557	+	0.102017i
$638$	−4.34295			−0.171939
$639$	14.7322			0.582798
$640$	0.623490	−	0.781831i	0.0246456	−	0.0309046i
$641$	−12.8963	−	6.21052i	−0.509372	−	0.245301i	0.161501	−	0.986873i	$-0.448366\pi$
$641$	−12.8963	−	6.21052i	−0.509372	−	0.245301i	−0.670874	+	0.741572i	$0.734081\pi$
$642$	2.92094	+	12.7975i	0.115280	+	0.505076i
$643$	−5.02164	+	22.0012i	−0.198034	+	0.867644i	0.774071	+	0.633099i	$0.218217\pi$
$643$	−5.02164	+	22.0012i	−0.198034	+	0.867644i	−0.972105	+	0.234546i	$0.924640\pi$
$644$	−21.7853			−0.858460
$645$	−7.87572	+	3.77558i	−0.310106	+	0.148663i
$646$	−19.7143			−0.775651
$647$	1.43062	−	6.26796i	0.0562435	−	0.246419i	−0.938989	−	0.343946i	$-0.888236\pi$
$647$	1.43062	−	6.26796i	0.0562435	−	0.246419i	0.995233	+	0.0975273i	$0.0310933\pi$
$648$	0.849788	+	3.72316i	0.0333828	+	0.146260i
$649$	−1.06259	−	0.511717i	−0.0417103	−	0.0200866i
$650$	−0.277479	+	0.347948i	−0.0108836	+	0.0136476i
$651$	−8.95901			−0.351131
$652$	−14.1908			−0.555754
$653$	12.7324	−	15.9660i	0.498259	−	0.624796i	−0.467577	−	0.883952i	$-0.654873\pi$
$653$	12.7324	−	15.9660i	0.498259	−	0.624796i	0.965835	+	0.259156i	$0.0834444\pi$
$654$	−5.78013	+	2.78356i	−0.226021	+	0.108846i
$655$	−11.8193	−	14.8210i	−0.461820	−	0.579104i
$656$	4.27658	−	2.05949i	0.166972	−	0.0804096i
$657$	3.88748	−	17.0321i	0.151665	−	0.664487i
$658$	8.19703	−	10.2787i	0.319553	−	0.400707i
$659$	6.34020	−	27.7782i	0.246979	−	1.08209i	−0.687533	−	0.726153i	$-0.741306\pi$
$659$	6.34020	−	27.7782i	0.246979	−	1.08209i	0.934512	−	0.355932i	$-0.115837\pi$
$660$	−2.92543	−	1.40881i	−0.113872	−	0.0548379i
$661$	2.73294	+	3.42700i	0.106299	+	0.133295i	0.832135	−	0.554573i	$-0.187118\pi$
$661$	2.73294	+	3.42700i	0.106299	+	0.133295i	−0.725836	+	0.687868i	$0.758547\pi$
$662$	3.04607	+	3.81965i	0.118389	+	0.148455i
$663$	−0.761035	−	3.33431i	−0.0295562	−	0.129494i
$664$	6.17428	+	2.97338i	0.239609	+	0.115389i
$665$	11.6820	−	5.62574i	0.453007	−	0.218157i
$666$	−1.03153	−	4.51943i	−0.0399710	−	0.175124i
$667$	2.27581	+	9.97097i	0.0881197	+	0.386078i
$668$	9.88586	−	4.76078i	0.382495	−	0.184200i
$669$	−29.6777	−	14.2920i	−1.14741	−	0.552562i
$670$	−0.381525	−	1.67157i	−0.0147396	−	0.0645783i
$671$	5.63242	+	7.06283i	0.217437	+	0.272657i
$672$	−3.15127	−	3.95157i	−0.121563	−	0.152435i
$673$	−38.2023	−	18.3973i	−1.47259	−	0.709163i	−0.486242	−	0.873824i	$-0.661633\pi$
$673$	−38.2023	−	18.3973i	−1.47259	−	0.709163i	−0.986350	+	0.164661i	$0.947347\pi$
$674$	−0.696781	+	3.05280i	−0.0268390	+	0.117589i
$675$	−3.50942	+	4.40068i	−0.135078	+	0.169382i
$676$	2.84870	−	12.4810i	0.109565	−	0.480037i
$677$	40.2563	−	19.3864i	1.54718	−	0.745081i	0.551172	−	0.834391i	$-0.314181\pi$
$677$	40.2563	−	19.3864i	1.54718	−	0.745081i	0.996004	+	0.0893105i	$0.0284664\pi$
$678$	−8.90281	−	11.1638i	−0.341910	−	0.428742i
$679$	38.0339	−	18.3162i	1.45961	−	0.702909i
$680$	−3.59738	+	4.51097i	−0.137953	+	0.172988i
$681$	−35.3794			−1.35574
$682$	4.32122			0.165468
$683$	−7.66423	+	9.61063i	−0.293263	+	0.367741i	−0.906534	−	0.422132i	$-0.861282\pi$
$683$	−7.66423	+	9.61063i	−0.293263	+	0.367741i	0.613271	+	0.789873i	$0.289853\pi$
$684$	3.77422	+	1.81757i	0.144311	+	0.0694964i
$685$	3.96553	+	17.3741i	0.151515	+	0.663831i
$686$	0.337701	−	1.47957i	0.0128935	−	0.0564901i
$687$	7.23144			0.275897
$688$	6.55743	+	0.0116118i	0.250000	+	0.000442697i
$689$	−0.356292			−0.0135736
$690$	−1.70149	+	7.45473i	−0.0647748	+	0.283797i
$691$	−1.11284	−	4.87565i	−0.0423343	−	0.185479i	0.949340	−	0.314251i	$-0.101753\pi$
$691$	−1.11284	−	4.87565i	−0.0423343	−	0.185479i	−0.991674	+	0.128773i	$0.958896\pi$
$692$	−21.7759	−	10.4867i	−0.827795	−	0.398645i
$693$	7.07137	−	8.86722i	0.268619	−	0.336838i
$694$	20.4134			0.774881
$695$	−8.34189			−0.316426
$696$	−1.47941	+	1.85512i	−0.0560768	+	0.0703181i
$697$	−24.6748	+	11.8827i	−0.934623	+	0.450091i
$698$	−17.4963	−	21.9397i	−0.662245	−	0.830429i
$699$	17.7694	−	8.55727i	0.672099	−	0.323666i
$700$	0.844405	−	3.69958i	0.0319155	−	0.139831i
$701$	29.4405	−	36.9173i	1.11195	−	1.39435i	0.202127	−	0.979359i	$-0.435215\pi$
$701$	29.4405	−	36.9173i	1.11195	−	1.39435i	0.909827	−	0.414987i	$-0.136214\pi$
$702$	−0.557414	+	2.44219i	−0.0210382	+	0.0921746i
$703$	11.6401	+	5.60556i	0.439013	+	0.211418i
$704$	1.51996	+	1.90597i	0.0572857	+	0.0718340i
$705$	−2.87709	−	3.60775i	−0.108357	−	0.135876i
$706$	5.27638	+	23.1173i	0.198579	+	0.870033i
$707$	−26.0613	−	12.5504i	−0.980134	−	0.472008i
$708$	−0.580550	+	0.279578i	−0.0218184	+	0.0105072i
$709$	2.63324	+	11.5370i	0.0988936	+	0.433281i	1.00000		0.000317035i	$-0.000100915\pi$
$709$	2.63324	+	11.5370i	0.0988936	+	0.433281i	−0.901106	+	0.433598i	$0.857244\pi$
$710$	2.67392	+	11.7152i	0.100350	+	0.439663i
$711$	4.70621	−	2.26639i	0.176497	−	0.0849962i
$712$	7.92684	+	3.81737i	0.297071	+	0.143062i
$713$	−2.26442	−	9.92107i	−0.0848032	−	0.371547i
$714$	18.1820	+	22.7996i	0.680446	+	0.853252i
$715$	−0.676446	−	0.848237i	−0.0252977	−	0.0317223i
$716$	5.22457	+	2.51602i	0.195251	+	0.0940281i
$717$	−2.32104	+	10.1691i	−0.0866809	+	0.379774i
$718$	9.96148	−	12.4913i	0.371759	−	0.466171i
$719$	−3.65436	+	16.0108i	−0.136284	+	0.597101i	0.859948	+	0.510381i	$0.170496\pi$
$719$	−3.65436	+	16.0108i	−0.136284	+	0.597101i	−0.996233	+	0.0867201i	$0.972361\pi$
$720$	1.10459	−	0.531942i	0.0411656	−	0.0198243i
$721$	24.4302	+	30.6345i	0.909828	+	1.14089i
$722$	6.59972	−	3.17826i	0.245616	−	0.118282i
$723$	−16.7185	+	20.9644i	−0.621769	+	0.779674i
$724$	−23.4185			−0.870342
$725$	−1.78148			−0.0661627
$726$	−4.19951	+	5.26602i	−0.155858	+	0.195440i
$727$	34.3277	+	16.5314i	1.27314	+	0.613114i	0.943619	−	0.331032i	$-0.107397\pi$
$727$	34.3277	+	16.5314i	1.27314	+	0.613114i	0.329525	+	0.944147i	$0.393111\pi$
$728$	−0.375796	−	1.64647i	−0.0139279	−	0.0610222i
$729$	−6.04651	+	26.4915i	−0.223945	+	0.981166i
$730$	14.2497			0.527405
$731$	−37.8347	−	0.0669973i	−1.39937	−	0.00247798i
$732$	4.93559			0.182425
$733$	7.71892	−	33.8188i	0.285105	−	1.24913i	−0.606050	−	0.795426i	$-0.707247\pi$
$733$	7.71892	−	33.8188i	0.285105	−	1.24913i	0.891155	−	0.453699i	$-0.149896\pi$
$734$	−6.03685	−	26.4492i	−0.222824	−	0.976257i
$735$	−8.88002	−	4.27639i	−0.327544	−	0.157737i
$736$	3.57942	−	4.48845i	0.131939	−	0.165446i
$737$	4.17979			0.153965
$738$	5.81940			0.214215
$739$	9.36745	−	11.7464i	0.344587	−	0.432099i	−0.579094	−	0.815261i	$-0.696594\pi$
$739$	9.36745	−	11.7464i	0.344587	−	0.432099i	0.923681	+	0.383162i	$0.125165\pi$
$740$	3.40666	−	1.64056i	0.125231	−	0.0603083i
$741$	−1.26279	−	1.58349i	−0.0463899	−	0.0581711i
$742$	2.73713	−	1.31813i	0.100483	−	0.0483901i
$743$	7.45681	−	32.6704i	0.273564	−	1.19856i	−0.632209	−	0.774798i	$-0.717852\pi$
$743$	7.45681	−	32.6704i	0.273564	−	1.19856i	0.905773	−	0.423764i	$-0.139291\pi$
$744$	1.47200	−	1.84583i	0.0539663	−	0.0676716i
$745$	4.16478	−	18.2471i	0.152586	−	0.668522i
$746$	−25.9140	−	12.4795i	−0.948779	−	0.456908i
$747$	5.23838	+	6.56873i	0.191662	+	0.240337i
$748$	−8.76978	−	10.9970i	−0.320655	−	0.402089i
$749$	−8.32197	−	36.4609i	−0.304078	−	1.33225i
$750$	−1.20001	−	0.577896i	−0.0438183	−	0.0211018i
$751$	−31.1182	+	14.9857i	−1.13552	+	0.546837i	−0.904653	−	0.426148i	$-0.859870\pi$
$751$	−31.1182	+	14.9857i	−1.13552	+	0.546837i	−0.230866	+	0.972986i	$0.574156\pi$
$752$	0.770935	+	3.37769i	0.0281131	+	0.123172i
$753$	4.35523	+	19.0815i	0.158714	+	0.695369i
$754$	−0.714320	+	0.343998i	−0.0260140	+	0.0125277i
$755$	−12.3802	−	5.96199i	−0.450562	−	0.216979i
$756$	−4.75288	−	20.8237i	−0.172861	−	0.757352i
$757$	−10.7612	−	13.4942i	−0.391123	−	0.490453i	0.546816	−	0.837253i	$-0.315840\pi$
$757$	−10.7612	−	13.4942i	−0.391123	−	0.490453i	−0.937939	+	0.346800i	$0.887268\pi$
$758$	0.764118	+	0.958173i	0.0277540	+	0.0348024i
$759$	−16.7947	−	8.08790i	−0.609609	−	0.293572i
$760$	−0.760321	+	3.33118i	−0.0275797	+	0.120835i
$761$	23.8520	−	29.9095i	0.864635	−	1.08422i	−0.131046	−	0.991376i	$-0.541834\pi$
$761$	23.8520	−	29.9095i	0.864635	−	1.08422i	0.995681	−	0.0928412i	$-0.0295949\pi$
$762$	1.81833	−	7.96661i	0.0658710	−	0.288600i
$763$	16.4680	−	7.93058i	0.596182	−	0.287106i
$764$	−1.68821	−	2.11695i	−0.0610773	−	0.0765885i
$765$	−6.37320	+	3.06917i	−0.230424	+	0.110966i
$766$	−18.1390	+	22.7456i	−0.655389	+	0.821831i
$767$	−0.215305			−0.00777421
$768$	1.33192			0.0480613
$769$	2.64511	−	3.31687i	0.0953852	−	0.119609i	−0.731848	−	0.681468i	$-0.761342\pi$
$769$	2.64511	−	3.31687i	0.0953852	−	0.119609i	0.827233	+	0.561858i	$0.189913\pi$
$770$	8.33476	+	4.01381i	0.300364	+	0.144648i
$771$	1.57940	+	6.91980i	0.0568807	+	0.249211i
$772$	−4.30103	+	18.8440i	−0.154797	+	0.678212i
$773$	4.09714			0.147364			0.0736819	−	0.997282i	$-0.476525\pi$
$773$	4.09714			0.147364			0.0736819	+	0.997282i	$0.476525\pi$
$774$	7.23709	+	3.50100i	0.260132	+	0.125841i
$775$	1.77257			0.0636726
$776$	−2.47544	+	10.8456i	−0.0888630	+	0.389334i
$777$	−4.25253	−	18.6315i	−0.152559	−	0.668403i
$778$	−7.22617	−	3.47994i	−0.259071	−	0.124762i
$779$	−10.1121	+	12.6802i	−0.362304	+	0.454315i
$780$	−0.592758			−0.0212241
$781$	−29.2941			−1.04822
$782$	−20.6523	+	25.8972i	−0.738525	+	0.926081i
$783$	−9.03437	+	4.35073i	−0.322862	+	0.155482i
$784$	4.61378	+	5.78550i	0.164778	+	0.206625i
$785$	−19.6442	+	9.46013i	−0.701130	+	0.337646i
$786$	5.61838	−	24.6157i	0.200401	−	0.878014i
$787$	27.2169	−	34.1289i	0.970177	−	1.21656i	−0.00608743	−	0.999981i	$-0.501938\pi$
$787$	27.2169	−	34.1289i	0.970177	−	1.21656i	0.976264	−	0.216582i	$-0.0694909\pi$
$788$	0.727457	−	3.18720i	0.0259146	−	0.113539i
$789$	31.7447	+	15.2874i	1.13014	+	0.544247i
$790$	2.65644	+	3.33106i	0.0945117	+	0.118514i
$791$	25.3648	+	31.8064i	0.901867	+	1.13091i
$792$	0.665067	+	2.91385i	0.0236321	+	0.103539i
$793$	1.48584	+	0.715545i	0.0527639	+	0.0254097i
$794$	−3.24161	+	1.56108i	−0.115041	+	0.0554006i
$795$	−0.237275	−	1.03957i	−0.00841528	−	0.0368698i
$796$	2.44516	+	10.7129i	0.0866664	+	0.379710i
$797$	−33.2872	+	16.0303i	−1.17909	+	0.567821i	−0.917647	−	0.397398i	$-0.869913\pi$
$797$	−33.2872	+	16.0303i	−1.17909	+	0.567821i	−0.261445	+	0.965218i	$0.584199\pi$
$798$	15.5594	+	7.49301i	0.550796	+	0.265250i
$799$	−4.44810	−	19.4884i	−0.157362	−	0.689450i
$800$	0.623490	+	0.781831i	0.0220437	+	0.0276419i
$801$	6.72529	+	8.43325i	0.237626	+	0.297974i
$802$	3.41458	+	1.64438i	0.120573	+	0.0580649i
$803$	−7.73000	+	33.8673i	−0.272786	+	1.19515i
$804$	1.42383	−	1.78542i	0.0502145	−	0.0629670i
$805$	4.84768	−	21.2391i	0.170858	−	0.748579i
$806$	0.710745	−	0.342277i	0.0250349	−	0.0120562i
$807$	11.4867	+	14.4038i	0.404349	+	0.507038i
$808$	6.86776	−	3.30734i	0.241607	−	0.116352i
$809$	9.12915	−	11.4476i	0.320964	−	0.402476i	−0.595007	−	0.803720i	$-0.702851\pi$
$809$	9.12915	−	11.4476i	0.320964	−	0.402476i	0.915971	+	0.401244i	$0.131422\pi$
$810$	−3.81891			−0.134183
$811$	17.4246			0.611862			0.305931	−	0.952054i	$-0.401032\pi$
$811$	17.4246			0.611862			0.305931	+	0.952054i	$0.401032\pi$
$812$	4.21494	−	5.28537i	0.147915	−	0.185480i
$813$	35.1314	+	16.9184i	1.23211	+	0.593354i
$814$	2.05113	+	8.98659i	0.0718921	+	0.314980i
$815$	3.15775	−	13.8350i	0.110611	−	0.484619i
$816$	−7.68481			−0.269022
$817$	−20.2041	+	9.68574i	−0.706852	+	0.338861i
$818$	5.88371			0.205719
$819$	0.460726	−	2.01857i	0.0160991	−	0.0705347i
$820$	1.05623	+	4.62764i	0.0368851	+	0.161604i
$821$	37.7299	+	18.1698i	1.31678	+	0.634129i	0.954576	−	0.297969i	$-0.0963091\pi$
$821$	37.7299	+	18.1698i	1.31678	+	0.634129i	0.362207	+	0.932098i	$0.382023\pi$
$822$	−14.7991	+	18.5575i	−0.516179	+	0.647268i
$823$	53.9922			1.88205			0.941025	−	0.338338i	$-0.109865\pi$
$823$	53.9922			1.88205			0.941025	+	0.338338i	$0.109865\pi$
$824$	−10.3256			−0.359711
$825$	2.02446	−	2.53859i	0.0704826	−	0.0883824i
$826$	1.65403	−	0.796539i	0.0575510	−	0.0277151i
$827$	−18.7799	−	23.5493i	−0.653043	−	0.818890i	0.339523	−	0.940598i	$-0.389734\pi$
$827$	−18.7799	−	23.5493i	−0.653043	−	0.818890i	−0.992566	+	0.121708i	$0.961163\pi$
$828$	6.34138	−	3.05385i	0.220378	−	0.106129i
$829$	0.686679	−	3.00854i	0.0238494	−	0.104491i	−0.961602	−	0.274447i	$-0.911505\pi$
$829$	0.686679	−	3.00854i	0.0238494	−	0.104491i	0.985452	+	0.169956i	$0.0543625\pi$
$830$	−4.27274	+	5.35784i	−0.148309	+	0.185973i
$831$	3.81471	−	16.7133i	0.132331	−	0.579779i
$832$	0.400969	+	0.193096i	0.0139011	+	0.00669441i
$833$	−26.6203	−	33.3808i	−0.922340	−	1.15658i
$834$	−6.92740	−	8.68668i	−0.239876	−	0.300795i
$835$	2.44161	+	10.6974i	0.0844952	+	0.370198i
$836$	−7.50479	−	3.61412i	−0.259559	−	0.124997i
$837$	8.98916	−	4.32895i	0.310711	−	0.149630i
$838$	−1.24280	−	5.44507i	−0.0429319	−	0.188097i
$839$	6.09941	+	26.7232i	0.210575	+	0.922589i	0.964177	+	0.265258i	$0.0854572\pi$
$839$	6.09941	+	26.7232i	0.210575	+	0.922589i	−0.753603	+	0.657330i	$0.771686\pi$
$840$	4.55372	−	2.19296i	0.157118	−	0.0756642i
$841$	23.2687	+	11.2056i	0.802369	+	0.386401i
$842$	6.05931	+	26.5476i	0.208818	+	0.914889i
$843$	13.9867	+	17.5388i	0.481729	+	0.604069i
$844$	13.4046	+	16.8089i	0.461407	+	0.578586i
$845$	11.5341	+	5.55455i	0.396787	+	0.191082i
$846$	−0.945168	+	4.14105i	−0.0324956	+	0.142372i
$847$	11.9647	−	15.0033i	0.411112	−	0.515518i
$848$	−0.178146	+	0.780508i	−0.00611755	+	0.0268027i
$849$	−16.2237	+	7.81294i	−0.556798	+	0.268140i
$850$	−3.59738	−	4.51097i	−0.123389	−	0.154725i
$851$	19.5574	−	9.41837i	0.670421	−	0.322858i
$852$	−9.97890	+	12.5131i	−0.341872	+	0.428693i
$853$	21.2952			0.729134			0.364567	−	0.931177i	$-0.381217\pi$
$853$	21.2952			0.729134			0.364567	+	0.931177i	$0.381217\pi$
$854$	−14.0619			−0.481187
$855$	−2.61184	+	3.27514i	−0.0893231	+	0.112008i
$856$	8.87942	+	4.27610i	0.303492	+	0.146154i
$857$	−2.95680	−	12.9546i	−0.101002	−	0.442520i	−0.999990	−	0.00454529i	$-0.998553\pi$
$857$	−2.95680	−	12.9546i	−0.101002	−	0.442520i	0.898987	−	0.437974i	$-0.144304\pi$
$858$	0.321552	−	1.40881i	0.0109776	−	0.0480960i
$859$	20.4042			0.696182			0.348091	−	0.937461i	$-0.386830\pi$
$859$	20.4042			0.696182			0.348091	+	0.937461i	$0.386830\pi$
$860$	−1.47049	+	6.39044i	−0.0501431	+	0.217912i
$861$	23.9907			0.817602
$862$	2.67362	−	11.7139i	0.0910638	−	0.398977i
$863$	1.63604	+	7.16797i	0.0556915	+	0.244001i	0.995110	−	0.0987715i	$-0.0314913\pi$
$863$	1.63604	+	7.16797i	0.0556915	+	0.244001i	−0.939419	+	0.342772i	$0.888634\pi$
$864$	5.07126	+	2.44219i	0.172528	+	0.0830850i
$865$	15.0694	−	18.8964i	0.512374	−	0.642497i
$866$	−4.35220			−0.147894
$867$	21.6968			0.736862
$868$	−4.19385	+	5.25892i	−0.142348	+	0.178499i
$869$	−9.35799	+	4.50657i	−0.317448	+	0.152875i
$870$	−1.47941	−	1.85512i	−0.0501566	−	0.0628944i
$871$	0.687483	−	0.331075i	0.0232945	−	0.0112180i
$872$	−1.07182	+	4.69595i	−0.0362964	+	0.159025i
$873$	−8.50357	+	10.6631i	−0.287802	+	0.360893i
$874$	−4.36496	+	19.1241i	−0.147647	+	0.646883i
$875$	3.41893	+	1.64647i	0.115581	+	0.0556608i
$876$	11.8335	+	14.8387i	0.399815	+	0.501352i
$877$	9.17147	+	11.5007i	0.309699	+	0.388350i	0.912184	−	0.409780i	$-0.134394\pi$
$877$	9.17147	+	11.5007i	0.309699	+	0.388350i	−0.602486	+	0.798130i	$0.705823\pi$
$878$	7.06575	+	30.9571i	0.238457	+	1.04475i
$879$	16.5883	+	7.98849i	0.559508	+	0.269445i
$880$	−2.19641	+	1.05773i	−0.0740409	+	0.0356562i
$881$	−0.544785	−	2.38686i	−0.0183543	−	0.0804153i	0.964921	−	0.262539i	$-0.0845599\pi$
$881$	−0.544785	−	2.38686i	−0.0183543	−	0.0804153i	−0.983276	+	0.182124i	$0.941703\pi$
$882$	2.01878	+	8.84487i	0.0679760	+	0.297822i
$883$	16.1442	−	7.77463i	0.543295	−	0.261637i	−0.142045	−	0.989860i	$-0.545368\pi$
$883$	16.1442	−	7.77463i	0.543295	−	0.261637i	0.685340	+	0.728223i	$0.259654\pi$
$884$	−2.31349	−	1.11412i	−0.0778110	−	0.0374718i
$885$	−0.143384	−	0.628206i	−0.00481980	−	0.0211169i
$886$	−10.9360	−	13.7133i	−0.367402	−	0.460707i
$887$	−10.6220	−	13.3196i	−0.356652	−	0.447227i	0.570845	−	0.821058i	$-0.306616\pi$
$887$	−10.6220	−	13.3196i	−0.356652	−	0.447227i	−0.927497	+	0.373831i	$0.878044\pi$
$888$	4.53739	+	2.18509i	0.152265	+	0.0733268i
$889$	−5.18054	+	22.6974i	−0.173750	+	0.761248i
$890$	−5.48554	+	6.87865i	−0.183876	+	0.230573i
$891$	2.07164	−	9.07643i	0.0694024	−	0.304072i
$892$	−22.2820	+	10.7304i	−0.746057	+	0.359282i
$893$	−7.38078	−	9.25521i	−0.246988	−	0.309714i
$894$	22.4599	−	10.8161i	0.751171	−	0.361745i
$895$	−3.61551	+	4.53371i	−0.120853	+	0.151545i
$896$	−3.79472			−0.126773
$897$	−3.40299			−0.113622
$898$	12.3026	−	15.4270i	0.410543	−	0.514804i
$899$	2.84508	+	1.37012i	0.0948888	+	0.0456961i
$900$	0.272811	+	1.19526i	0.00909371	+	0.0398421i
$901$	1.02786	−	4.50333i	0.0342428	−	0.150028i
$902$	−11.5715			−0.385289
$903$	29.8352	+	14.4330i	0.992855	+	0.480301i
$904$	−10.7207			−0.356564
$905$	5.21111	−	22.8314i	0.173223	−	0.758940i
$906$	−4.07254	−	17.8430i	−0.135301	−	0.592793i
$907$	−35.5323	−	17.1115i	−1.17983	−	0.568177i	−0.261970	−	0.965076i	$-0.584372\pi$
$907$	−35.5323	−	17.1115i	−1.17983	−	0.568177i	−0.917862	+	0.396899i	$0.870086\pi$
$908$	−16.5616	+	20.7676i	−0.549617	+	0.689198i
$909$	9.34537			0.309966
$910$	1.68881			0.0559835
$911$	−34.6135	+	43.4040i	−1.14680	+	1.43804i	−0.266361	+	0.963873i	$0.585821\pi$
$911$	−34.6135	+	43.4040i	−1.14680	+	1.43804i	−0.880436	+	0.474165i	$0.842750\pi$
$912$	−4.10027	+	1.97459i	−0.135773	+	0.0653851i
$913$	−10.4162	−	13.0615i	−0.344726	−	0.432272i
$914$	10.8583	−	5.22906i	0.359159	−	0.172962i
$915$	−1.09827	+	4.81184i	−0.0363077	+	0.159075i
$916$	3.38515	−	4.24484i	0.111848	−	0.140254i
$917$	−16.0072	+	70.1320i	−0.528604	+	2.31596i
$918$	−29.2599	−	14.0908i	−0.965720	−	0.465066i
$919$	−11.9033	−	14.9263i	−0.392654	−	0.492373i	0.545733	−	0.837959i	$-0.316251\pi$
$919$	−11.9033	−	14.9263i	−0.392654	−	0.492373i	−0.938387	+	0.345586i	$0.887680\pi$
$920$	3.57942	+	4.48845i	0.118010	+	0.147980i
$921$	−6.02504	−	26.3974i	−0.198532	−	0.869824i
$922$	6.42541	+	3.09431i	0.211609	+	0.101906i
$923$	−4.81823	+	2.32034i	−0.158594	+	0.0763748i
$924$	2.74177	+	12.0125i	0.0901975	+	0.395181i
$925$	0.841377	+	3.68631i	0.0276643	+	0.121205i
$926$	35.4733	−	17.0830i	1.16572	−	0.561383i
$927$	−11.4056	−	5.49265i	−0.374609	−	0.180402i
$928$	0.396418	+	1.73682i	0.0130130	+	0.0570139i
$929$	−23.6367	−	29.6395i	−0.775496	−	0.972441i	0.224502	−	0.974474i	$-0.427924\pi$
$929$	−23.6367	−	29.6395i	−0.775496	−	0.972441i	−0.999998	+	0.00203257i	$0.999353\pi$
$930$	1.47200	+	1.84583i	0.0482689	+	0.0605273i
$931$	−22.7805	−	10.9705i	−0.746601	−	0.359544i
$932$	3.29501	−	14.4364i	0.107932	−	0.472879i
$933$	−22.1132	+	27.7291i	−0.723955	+	0.907811i
$934$	−7.23710	+	31.7078i	−0.236805	+	1.03751i
$935$	12.6727	−	6.10285i	0.414442	−	0.199585i
$936$	0.340190	+	0.426585i	0.0111195	+	0.0139434i
$937$	−9.64509	+	4.64483i	−0.315091	+	0.151740i	−0.584745	−	0.811217i	$-0.698805\pi$
$937$	−9.64509	+	4.64483i	−0.315091	+	0.151740i	0.269653	+	0.962958i	$0.413091\pi$
$938$	−4.05659	+	5.08680i	−0.132452	+	0.166090i
$939$	21.8481			0.712987
$940$	−3.46455			−0.113001
$941$	−14.6809	+	18.4092i	−0.478583	+	0.600124i	−0.961249	−	0.275680i	$-0.911097\pi$
$941$	−14.6809	+	18.4092i	−0.478583	+	0.600124i	0.482666	+	0.875804i	$0.339668\pi$
$942$	−26.1643	−	12.6001i	−0.852480	−	0.410533i
$943$	6.06374	+	26.5670i	0.197462	+	0.865140i
$944$	−0.107653	+	0.471656i	−0.00350379	+	0.0153511i
$945$	21.3593			0.694817
$946$	−14.3905	−	6.96152i	−0.467875	−	0.226338i
$947$	−27.4270			−0.891256			−0.445628	−	0.895218i	$-0.647020\pi$
$947$	−27.4270			−0.891256			−0.445628	+	0.895218i	$0.647020\pi$
$948$	−1.26275	+	5.53247i	−0.0410122	+	0.179686i
$949$	1.41116	+	6.18271i	0.0458083	+	0.200699i
$950$	−3.07848	−	1.48252i	−0.0998789	−	0.0480992i
$951$	20.6703	−	25.9197i	0.670281	−	0.840505i
$952$	21.8946			0.709607
$953$	−33.6266			−1.08927			−0.544637	−	0.838672i	$-0.683332\pi$
$953$	−33.6266			−1.08927			−0.544637	+	0.838672i	$0.683332\pi$
$954$	−0.611963	+	0.767378i	−0.0198130	+	0.0248448i
$955$	2.43953	−	1.17482i	0.0789415	−	0.0380162i
$956$	4.88275	+	6.12278i	0.157920	+	0.198025i
$957$	5.21160	−	2.50978i	0.168467	−	0.0811295i
$958$	−0.973014	+	4.26305i	−0.0314366	+	0.137733i
$959$	42.1638	−	52.8718i	1.36154	−	1.70732i
$960$	−0.296379	+	1.29852i	−0.00956559	+	0.0419096i
$961$	25.0992	+	12.0871i	0.809651	+	0.389908i
$962$	1.04918	+	1.31563i	0.0338269	+	0.0424176i
$963$	7.53348	+	9.44668i	0.242763	+	0.304415i
$964$	4.47985	+	19.6275i	0.144286	+	0.632159i
$965$	−17.4145	−	8.38638i	−0.560593	−	0.269967i
$966$	26.1426	−	12.5896i	0.841126	−	0.405065i
$967$	−2.76785	−	12.1268i	−0.0890081	−	0.389970i	0.910726	−	0.413010i	$-0.135523\pi$
$967$	−2.76785	−	12.1268i	−0.0890081	−	0.389970i	−0.999735	+	0.0230401i	$0.992665\pi$
$968$	1.12529	+	4.93021i	0.0361681	+	0.158463i
$969$	23.6575	−	11.3928i	0.759988	−	0.365991i
$970$	−10.0228	−	4.82674i	−0.321814	−	0.154977i
$971$	−3.98586	−	17.4632i	−0.127912	−	0.560420i	−0.997748	−	0.0670781i	$-0.978632\pi$
$971$	−3.98586	−	17.4632i	−0.127912	−	0.560420i	0.869836	−	0.493342i	$-0.164225\pi$
$972$	7.35691	+	9.22527i	0.235973	+	0.295901i
$973$	19.7367	+	24.7490i	0.632729	+	0.793417i
$974$	−17.7852	−	8.56491i	−0.569875	−	0.274437i
$975$	0.131901	−	0.577896i	0.00422421	−	0.0185075i
$976$	2.31042	−	2.89718i	0.0739549	−	0.0927365i
$977$	−8.36260	+	36.6389i	−0.267543	+	1.17218i	0.645318	+	0.763914i	$0.276725\pi$
$977$	−8.36260	+	36.6389i	−0.267543	+	1.17218i	−0.912861	+	0.408270i	$0.866132\pi$
$978$	17.0291	−	8.20080i	0.544532	−	0.262233i
$979$	−13.3728	−	16.7690i	−0.427397	−	0.535939i
$980$	−6.66710	+	3.21071i	−0.212973	+	0.102562i
$981$	−3.68190	+	4.61696i	−0.117554	+	0.147408i
$982$	−22.2523			−0.710101
$983$	25.2854			0.806479			0.403239	−	0.915095i	$-0.367884\pi$
$983$	25.2854			0.806479			0.403239	+	0.915095i	$0.367884\pi$
$984$	−3.94178	+	4.94284i	−0.125659	+	0.157572i
$985$	2.94541	+	1.41844i	0.0938486	+	0.0451951i
$986$	−2.28723	−	10.0210i	−0.0728402	−	0.319134i
$987$	−3.89650	+	17.0717i	−0.124027	+	0.543397i
$988$	−1.52064			−0.0483781
$989$	−8.44197	+	36.6871i	−0.268439	+	1.16658i
$990$	−2.98878			−0.0949897
$991$	10.1525	−	44.4810i	0.322505	−	1.41298i	−0.510576	−	0.859833i	$-0.670568\pi$
$991$	10.1525	−	44.4810i	0.322505	−	1.41298i	0.833080	−	0.553152i	$-0.186575\pi$
$992$	−0.394434	−	1.72813i	−0.0125233	−	0.0548681i
$993$	−5.86269	−	2.82332i	−0.186047	−	0.0895955i
$994$	28.4306	−	35.6509i	0.901765	−	1.13078i
$995$	−10.9884			−0.348357
$996$	−9.12753			−0.289217
$997$	−9.90529	+	12.4208i	−0.313704	+	0.393372i	−0.913539	−	0.406752i	$-0.866661\pi$
$997$	−9.90529	+	12.4208i	−0.313704	+	0.393372i	0.599835	+	0.800124i	$0.295233\pi$
$998$	24.0534	−	11.5835i	0.761398	−	0.366670i
$999$	13.2695	+	16.6394i	0.419829	+	0.526449i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	430.2.k.a.121.1	✓	12
43.16	even	7	inner	430.2.k.a.231.1	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
430.2.k.a.121.1	✓	12	1.1	even	1	trivial
430.2.k.a.231.1	yes	12	43.16	even	7	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 430 = 2 \cdot 5 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	430.k (of order \(7\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.222521 + 0.974928i) q^{2} +(-0.296379 - 1.29852i) q^{3} +(-0.900969 - 0.433884i) q^{4} +(0.623490 - 0.781831i) q^{5} +1.33192 q^{6} -3.79472 q^{7} +(0.623490 - 0.781831i) q^{8} +(1.10459 - 0.531942i) q^{9} +O(q^{10})\)	\(q+(-0.222521 + 0.974928i) q^{2} +(-0.296379 - 1.29852i) q^{3} +(-0.900969 - 0.433884i) q^{4} +(0.623490 - 0.781831i) q^{5} +1.33192 q^{6} -3.79472 q^{7} +(0.623490 - 0.781831i) q^{8} +(1.10459 - 0.531942i) q^{9} +(0.623490 + 0.781831i) q^{10} +(-2.19641 + 1.05773i) q^{11} +(-0.296379 + 1.29852i) q^{12} +(-0.277479 + 0.347948i) q^{13} +(0.844405 - 3.69958i) q^{14} +(-1.20001 - 0.577896i) q^{15} +(0.623490 + 0.781831i) q^{16} +(-3.59738 - 4.51097i) q^{17} +(0.272811 + 1.19526i) q^{18} +(-3.07848 - 1.48252i) q^{19} +(-0.900969 + 0.433884i) q^{20} +(1.12468 + 4.92753i) q^{21} +(-0.542468 - 2.37671i) q^{22} +(-5.17241 + 2.49090i) q^{23} +(-1.20001 - 0.577896i) q^{24} +(-0.222521 - 0.974928i) q^{25} +(-0.277479 - 0.347948i) q^{26} +(-3.50942 - 4.40068i) q^{27} +(3.41893 + 1.64647i) q^{28} +(0.396418 - 1.73682i) q^{29} +(0.830435 - 1.04133i) q^{30} +(-0.394434 + 1.72813i) q^{31} +(-0.900969 + 0.433884i) q^{32} +(2.02446 + 2.53859i) q^{33} +(5.19836 - 2.50340i) q^{34} +(-2.36597 + 2.96683i) q^{35} -1.22600 q^{36} -3.78111 q^{37} +(2.13037 - 2.67140i) q^{38} +(0.534056 + 0.257188i) q^{39} +(-0.222521 - 0.974928i) q^{40} +(1.05623 - 4.62764i) q^{41} -5.05425 q^{42} +(4.09757 - 5.11956i) q^{43} +2.43783 q^{44} +(0.272811 - 1.19526i) q^{45} +(-1.27748 - 5.59700i) q^{46} +(3.12145 + 1.50321i) q^{47} +(0.830435 - 1.04133i) q^{48} +7.39993 q^{49} +1.00000 q^{50} +(-4.79140 + 6.00822i) q^{51} +(0.400969 - 0.193096i) q^{52} +(0.499153 + 0.625919i) q^{53} +(5.07126 - 2.44219i) q^{54} +(-0.542468 + 2.37671i) q^{55} +(-2.36597 + 2.96683i) q^{56} +(-1.01268 + 4.43685i) q^{57} +(1.60506 + 0.772957i) q^{58} +(0.301636 + 0.378239i) q^{59} +(0.830435 + 1.04133i) q^{60} +(-0.824581 - 3.61273i) q^{61} +(-1.59703 - 0.769089i) q^{62} +(-4.19161 + 2.01857i) q^{63} +(-0.222521 - 0.974928i) q^{64} +(0.0990311 + 0.433884i) q^{65} +(-2.92543 + 1.40881i) q^{66} +(-1.54476 - 0.743918i) q^{67} +(1.28389 + 5.62508i) q^{68} +(4.76748 + 5.97823i) q^{69} +(-2.36597 - 2.96683i) q^{70} +(10.8265 + 5.21375i) q^{71} +(0.272811 - 1.19526i) q^{72} +(8.88454 - 11.1409i) q^{73} +(0.841377 - 3.68631i) q^{74} +(-1.20001 + 0.577896i) q^{75} +(2.13037 + 2.67140i) q^{76} +(8.33476 - 4.01381i) q^{77} +(-0.369579 + 0.463437i) q^{78} +4.26059 q^{79} +1.00000 q^{80} +(-2.38105 + 2.98575i) q^{81} +(4.27658 + 2.05949i) q^{82} +(1.52492 + 6.68112i) q^{83} +(1.12468 - 4.92753i) q^{84} -5.76974 q^{85} +(4.07941 + 5.13404i) q^{86} -2.37279 q^{87} +(-0.542468 + 2.37671i) q^{88} +(1.95777 + 8.57754i) q^{89} +(1.10459 + 0.531942i) q^{90} +(1.05296 - 1.32037i) q^{91} +5.74094 q^{92} +2.36091 q^{93} +(-2.16011 + 2.70869i) q^{94} +(-3.07848 + 1.48252i) q^{95} +(0.830435 + 1.04133i) q^{96} +(-10.0228 + 4.82674i) q^{97} +(-1.64664 + 7.21440i) q^{98} +(-1.86348 + 2.33672i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 2 q^{2} - q^{3} - 2 q^{4} - 2 q^{5} - 8 q^{6} + 4 q^{7} - 2 q^{8} + 7 q^{9}+O(q^{10}) \) 12 * q - 2 * q^2 - q^3 - 2 * q^4 - 2 * q^5 - 8 * q^6 + 4 * q^7 - 2 * q^8 + 7 * q^9	\( 12 q - 2 q^{2} - q^{3} - 2 q^{4} - 2 q^{5} - 8 q^{6} + 4 q^{7} - 2 q^{8} + 7 q^{9} - 2 q^{10} + 3 q^{11} - q^{12} - 4 q^{13} - 10 q^{14} - q^{15} - 2 q^{16} - 5 q^{17} - 2 q^{19} - 2 q^{20} + 22 q^{21} - 4 q^{22} - 16 q^{23} - q^{24} - 2 q^{25} - 4 q^{26} + 8 q^{27} + 11 q^{28} + 2 q^{29} + 6 q^{30} + 27 q^{31} - 2 q^{32} + 6 q^{33} + 2 q^{34} - 3 q^{35} - 18 q^{37} - 2 q^{38} + 5 q^{39} - 2 q^{40} + 14 q^{41} - 20 q^{42} + 14 q^{43} - 4 q^{44} - 16 q^{46} + 2 q^{47} + 6 q^{48} - 12 q^{49} + 12 q^{50} - 5 q^{51} - 4 q^{52} + 2 q^{53} - 6 q^{54} - 4 q^{55} - 3 q^{56} - 19 q^{57} + 2 q^{58} + 4 q^{59} + 6 q^{60} + 16 q^{61} - 22 q^{62} + 13 q^{63} - 2 q^{64} + 10 q^{65} - 8 q^{66} + 9 q^{67} + 9 q^{68} - 15 q^{69} - 3 q^{70} + 27 q^{71} + 28 q^{73} + 24 q^{74} - q^{75} - 2 q^{76} + 26 q^{77} + 5 q^{78} + 10 q^{79} + 12 q^{80} - 12 q^{81} + 7 q^{82} - 31 q^{83} + 22 q^{84} - 12 q^{85} - 28 q^{86} - 6 q^{87} - 4 q^{88} - 38 q^{89} + 7 q^{90} + 8 q^{91} + 12 q^{92} - 2 q^{93} - 12 q^{94} - 2 q^{95} + 6 q^{96} - 15 q^{97} - 19 q^{98} - 6 q^{99}+O(q^{100}) \) 12 * q - 2 * q^2 - q^3 - 2 * q^4 - 2 * q^5 - 8 * q^6 + 4 * q^7 - 2 * q^8 + 7 * q^9 - 2 * q^10 + 3 * q^11 - q^12 - 4 * q^13 - 10 * q^14 - q^15 - 2 * q^16 - 5 * q^17 - 2 * q^19 - 2 * q^20 + 22 * q^21 - 4 * q^22 - 16 * q^23 - q^24 - 2 * q^25 - 4 * q^26 + 8 * q^27 + 11 * q^28 + 2 * q^29 + 6 * q^30 + 27 * q^31 - 2 * q^32 + 6 * q^33 + 2 * q^34 - 3 * q^35 - 18 * q^37 - 2 * q^38 + 5 * q^39 - 2 * q^40 + 14 * q^41 - 20 * q^42 + 14 * q^43 - 4 * q^44 - 16 * q^46 + 2 * q^47 + 6 * q^48 - 12 * q^49 + 12 * q^50 - 5 * q^51 - 4 * q^52 + 2 * q^53 - 6 * q^54 - 4 * q^55 - 3 * q^56 - 19 * q^57 + 2 * q^58 + 4 * q^59 + 6 * q^60 + 16 * q^61 - 22 * q^62 + 13 * q^63 - 2 * q^64 + 10 * q^65 - 8 * q^66 + 9 * q^67 + 9 * q^68 - 15 * q^69 - 3 * q^70 + 27 * q^71 + 28 * q^73 + 24 * q^74 - q^75 - 2 * q^76 + 26 * q^77 + 5 * q^78 + 10 * q^79 + 12 * q^80 - 12 * q^81 + 7 * q^82 - 31 * q^83 + 22 * q^84 - 12 * q^85 - 28 * q^86 - 6 * q^87 - 4 * q^88 - 38 * q^89 + 7 * q^90 + 8 * q^91 + 12 * q^92 - 2 * q^93 - 12 * q^94 - 2 * q^95 + 6 * q^96 - 15 * q^97 - 19 * q^98 - 6 * q^99

Introduction

L-functions

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